Alg 1 (7): Linear Equations
Slope = 2 y-intercept = -1 The easiest way to find the slope and y-intercept of a line is to make sure the equation is in slope-intercept form: 2x − y -2x = 1 -2x -y/-1 = (1 - 2x)/-1 y = 2x - 1 Recall the slope-intercept form of a line: y = mx + b y = dependent variable x = independent variable m = slope (∆y/∆x) b = y-intercept (where the line hits the y-axis) In this case, y = 2x - 1 has... 1) m = 2 = slope 2) b = -1 = y-intercept
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Find the slope and y-intercept of the following equation: 2x − y = 1
Slope = -8/3 y-intercept = -3
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Find the slope and y-intercept of the following equation: 8x + 3y = −9
Slope = -1/2 y-intercept = -4
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Find the slope and y-intercept of the following equation: x + 2y = −8
Slope = -5/2 y-intercept = -5 Recall the slope-intercept form of a line: y = mx + b y = dependent variable x = independent variable m = slope (∆y/∆x) b = y-intercept (where the line hits the y-axis) In this case, y = − 5/2 x − 5 has... 1) m = -5/2 = slope 2) b = -5 = y-intercept
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Find the slope and y-intercept of the following equation: y = − 5/2 x − 5
Your line should have the following: 1) y-intercept at 5 2) Passes through point (-3,-5)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: 10x - 3y = -15
Your line should have the following: 1) y-intercept at 0 2) Passes through point (1,-4)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: 4x + y = 0
Your line should have the following: 1) y-intercept at -5 2) Passes through point (-2,2)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: 7x + 2y = -10
Your graph should be a vertical line through the point (5,0)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: x = 5
Your line should have the following: 1) y-intercept at -1 2) Passes through point (4,0) To graph a linear function... 1) Plot the y-intercept. You should have a point at (0,-1) 2) Use the slope to plot another point, and connect the dots. In this case, our slope is 1/4, so we go up 1 and 4 to the right from the y-intercept for our next point at (4,0)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: y = 1/4x - 1
Your graph should be a horizontal line through the point (0,4)
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Sketch the graph of the following equation: y = 4
x = 2
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Write the equation of the line through the given point with the given slope. through: (2, 5), slope = undefined
y = 7x - 5 To find the slope-intercept form using (1) the slope and (2) a point... 1) Substitute the numbers into y = mx + b In this case, we know... a) m = slope = 7 b) (1,2) gives us x = 1 and y = 2, respectively Therefore, y = mx + b turns into: 2 -7 = 7(1) + b -7 -5 = b 2) Substitute m and b into the equation Therefore, y = mx + b turns into: y = 7x - 5
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of the line through the given point with the given slope. through: (1, 2), slope = 7
y = -x + 2
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of the line through the given point with the given slope. through: (3, −1), slope = −1
y = 5/3x
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Write the standard form of the equation of the line through the given point with the given slope. through: (3, 5), slope = 5/3
y = -4x - 3
From "Free Algebra 1 Worksheets" by Kuta Software LLC¹: Write the standard form of the equation of the line through the given point with the given slope. through: (−2, 5), slope = −4
y = -1
From "Free Pre-Algebra Worksheets" by Kuta Software LLC¹: Write the equation of this line.
y = -3/2x + 4 To find the slope-intercept form (y = mx + b) of a line... 1) Find the y-intercept (b) In this case, the line hits the y-axis at (0,4), so b = 4 2) Find the slope (m) In this case, we had to travel down 6 and right 4 to get to point B, so our slope would be m = -6/4 = -3/2 3) Substitute into y = mx + b y = -3/2x + 4
From "Free Pre-Algebra Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of this line.
y = 1/2x + 2
From "Free Pre-Algebra Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of this line.
y = 3x + 4
From "Free Pre-Algebra Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of this line.
y = 5/3x + 3
From "Free Pre-Algebra Worksheets" by Kuta Software LLC¹: Write the slope-intercept form of the equation of this line.
-b/a
From The College Panda ACT Math: Advanced Guide and Workbook (p. 71):¹ In the standard (x,y) coordinate plane, what is the x-intercept of the line represented by y = ax + b, where a and b are constants?
y = 1/2x + 3
From The College Panda ACT Math: Advanced Guide and Workbook (p. 72):¹ Write the equation of the line graphed in the standard (x,y) coordinate plane
7
From The College Panda ACT Math: Advanced Guide and Workbook (p. 73):¹ Find the y-intercept of the line that passes through (-2,3) and (3,13) in the standard (x,y) coordinate plane
x = -4
From The College Panda ACT Math: Advanced Guide and Workbook (p. 75):¹ A line in the standard (x,y) coordinate plane is parallel to the y-axis and 4 units to the left of it. What is the equation of this line?
h = -8t + 120
From The College Panda ACT Math: Advanced Guide and Workbook (p. 75):¹ An elevator is lowered at a constant speed towards the ground. The table shows the height, h meters, of the elevator at 1-second intervals from t = 0 seconds to t = 4 seconds. Write an equation that represents the data.
y = 6x - 10
From The College Panda ACT Math: Advanced Guide and Workbook (p. 75):¹ What is the slope-intercept equation of the line that passes through the points (2,2) and (-1, -4)?
y = -1/3x - 13/3
From The College Panda ACT Math: Advanced Guide and Workbook (p. 75):¹ Write an equation of the line that passes through (-4,-3) and (5, -6) in the standard (x,y) coordinate plane.
Your line should have the following: 1) y-intercept at 10 2) Passes through point (5,12)
From The College Panda ACT Math: Advanced Guide and Workbook (p. 76):¹ At her last gas station visit, Janelle pumped air into one of her car's tires. The relationship between the tire pressure, y pounds per square inch, and the time she spent pumping air into the tire, x seconds, was given by the equation 5y - 2x = 50. Draw a line that models this equation.
y = 1/2x + 2
From The College Panda ACT Math: Advanced Guide and Workbook (p. 77):¹ While doing a math assignment, Lia encountered a question that required her to graph the line y = 2x - 4 in the standard (x,y) coordinate plane. However, she mistakenly swapped the x and y coordinates of all her points. For example, she plotted (2,3) instead of (3,2). What is the equation of the line that Lia mistakenly graphed for this question?
1) Graphically, it's where the graph hits the x-axis 2) Algebraically, plug in 0 for y and solve for x
How do you find the x-intercept of a function?
m = (y₂ - y₁) / (x₂ - x₁) Or "rise over run"
Review: What is the equation for slope?
Your graph should be a vertical line through the point (-6,0)
Sketch the graph of the following equation: x = -6
Your graph should be a vertical line through the point (6.75,0)
Sketch the graph of the following equation: x = 6.75
Your graph should be a horizontal line through the point (0,-3)
Sketch the graph of the following equation: y = -3
Your graph should be a horizontal line through the point (0,2.5)
Sketch the graph of the following equation: y = 2.5
1) Graphically, it's where the graph hits the y-axis 2) Algebraically, plug in 0 for x and solve for y
What is a y-intercept and how do you find it?
y = # # = where the horizontal line hits the y axis The horizontal line that passes through (0,3) would be: y = 3
What is the equation of a horizontal line? Use your knowledge to find the equation of the horizontal line that passes through (0,3)
x = # # = where the vertical line hits the x-axis The vertical line that passes through (3,0) would be: x = 3
What is the equation of a vertical line? Use your knowledge to find the equation of the vertical line that passes through (3, 0)
y₂ - y₁ = m(x₂ - x₁)
What is the point-slope equation of a line?
y = mx + b y = dependent variable x = independent variable m = slope (∆y/∆x) b = y-intercept (where the line hits the y-axis)
What is the slope-intercept form of a line? What do all of the variables mean?
x = -2
Write the equation of this line.
x = 1
Write the equation of this line.
x = 3.5
Write the equation of this line.
y = -4
Write the equation of this line.
y = 1
Write the equation of this line.
