R. Point-Slope Form of a Line (problems with answers)

Which steps should be used to graph the equation y - 4 = 1/3 (x + 2)?

1. Plot the point (-2,4). 2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

The equation of a linear function in point-slope form is y - y1 = m(x - x1). Harold correctly wrote the equation y = 3(x - 7) using a point and the slope. Which point did Harold use?

When Harold wrote his equation, the point he used was (7, 0).

Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?

y - 7 = 4(x - 1)

What is the slope of the line?

5/2

Which equation represents a line that passes through (2, -1/2) and has a slope of 3?

y + 1/2 = 3(x - 2)

Which equation represents a line that passes through (-9, -3) and has a slope of -6?

y + 3 = -6(x + 9)

What is the equation of the graphed line in point-slope form?

y + 3 = 2 (x + 3)

What is the equation of the graphed line in point-slope form?

y + 6 = 3/4 (x + 4)

Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?

y - 1 = 1/2(x -5)

What is the equation of the graphed line in point-slope form?

y - 1 = 2/3 (x - 3)

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3 ?

y - 2 = 1/3(x - 3)

Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?

y - 4 = 2/5(x + 2)

Alejandra correctly wrote the equation y - 3 = 1/5 (x - 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

y - 3 = 2(x - 10)

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5). Step 2: Choose another point on the line, such as (1, 3). Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is 1/2 Step 4: Substitute those values into the point-slope form. y - y1 = m(x - x1) y - 3 = (x - 1) Which of Talia's steps is incorrect?

Step 3 is incorrect because it shows an incorrect ratio for the slope.

Anya graphed the line (y - 2) = 3(x - 1) on the coordinate grid.

The slope of her line is 3

What is the slope of the line?

-1/2

Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?

f(x) = -3x + 14

Which equations and/or functions represent the graphed line? Check all that apply.

f(x) = 0.5x + 2 f(x) = 1/2x + 2 y - 3 = 1/2(x - 2) y - 1 = 0.5(x + 2)

Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?

y - 1/3 = 3/4 (x - 4)

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x = 0 representing the year 2000, the graph below models this scenario. What number will complete the point-slope equation that models this scenario?

y 50,000 = -3,000 (x 10)