Algebra 1

Solve a multi-step inequality.

-0.6(x-5)<_15. Distribute -0.6x+3<_15. Subtract 3 from each side -0.6x<_12. Divide each side by -0.6= x>_-20

Solve an inequality using division -3x>24

-3x/-3<24/-3=x<-8

X/-6<7

-6*x/-6>-6*7= x>-42

Solve a two step inequality

3x-7<8. Add 7 to each side. 3x<15= divide each side by 3. X<5

Determine whether lines are perpendicular?

Line a= 12y=-7x+42, Line b: 11y=16x-52. Line a: y= -7/12x+42/12. Line b: 11y=16x-52 y=16/11x-52/11. The slope of line a is -7/12. The slope of line b is 16/11. The two slopes are not negative reciprocals, so lines a and b are not perpendicular

Solve |x-3|=8

Rewrite as 2 equations x-3=8 or x-3=-8. Add 3 to each side: x=11 or x=-5.

Solve 3|2x-7|-5=4

Rewrite the equation in form |ax+b|=c. Add 5 to each side 3|2x-7|=9. Divide each side by 3 |2x-7|=3. |2x-7|=3. 2x-7=3 or 2x-7=-3. Add 7 to each side= 2x=10 or 2x=4. Divide each side by 2 x=5 or x=2

Write an equation in point-slope form of the line that passes through the point (4,-3) and has a slope of 2. Formula= y-y1=m(x-x1)

y+3=2(x-4)

Determine which lines if any are parallel or perpendicular? Line a- y= 5x-3 Line b- x+5y=2 Line c- -10y-2x=0

Find the slopes Line a- it's already in slope intercept form the slope is 5. Line b- x+5y=2 5y=-x+2 y=-1/5x+2/5. Line c- -10y-2x=0 -10y=2x y=-1/5x. Lines b and c have slopes of -1/5 so they are parallel. Line a has a slope of 5 the negative reciprocal of -1/5 so its perpendicular to lines b and c.

Graph the equation y+2=2/3(x-3)

Because the equation is in point-slope form you know that the line has a slope of 2/3 and passes through the point (3,-2). Plot the point (3,-2) find the second point by using the slope.

Solve an absolute value equation? |x|=7

Distance between x and 0 is 7, so x=7 or x=-7. Solutions are 7 and -7

Using slope and y-intercept to write an equation. Write an equation of the line with a slope of -2 and y-intercept of 5?

Formula- y=mx+b y=-2x+5

Solve inequalities using multiplication? Solve x/4<5

4*x/4<4*5= x<20

How to calculate a slope?

M= y2-y1/x2-x1

What is a scatter plot going down hill?

Negative correlation

What is a scatter plot that is going uphill?

Positive correlation

What is a scatter plot all over mean?

Relatively no correlation

Write an equation of a line given two points. (3,-1) (0,-5) M=y2-y1/x2-x1

Step 1) calculate the slope) m=-1-(-5)/3-0= 4/3. Step 2) write slope-intercept form and substitute) y= 4/3x-5

Write an equation of the line that passes through (-2,5) and (2,-1)

Step 1) calculate the slope. Slope= -3/2. Step 2) find the y-intercept. Use the slope and point (-2,5) 5=-3/2(-2)+b, 2=b. Step 3) write an equation of the line. Y=-3/2x+2.

Write an equation in standard form of the points (1,1) and (2,-2)

Step 1) calculate the slope= -3. Step 2) write an equation in point slope form use (1,1) y-1=-3(x-1) Step 3) rewrite the equation in standard form 3x+y=4

Write an equation in point slope form of the points (-1,3) and (1,1)

Step 1) find the slope=-1. Step 2) write the equation in point slope form using either point. y-3=-1(x+1)

Find the missing coefficient in the equation of (-1,0) using ax+3y=2

Step 1) find value of a. Substitute the coordinates of the given point for x and y. A(-1)+3(0)=2, -A=2, A=-2. Step 2) complete the equation -2x+3y=2.

Write an equation of the line that passes through (4,-5) and is perpendicular to the line y=2x+3

Step 1) identify the slope the slope of the perpendicular line through (4,-5) is -1/2. Step 2) find the y- intercept -5=-1/2(4)+b -3=b. Step 3) write an equation y=-1/2x-3

Write an equation of the line that passes through the point (-1,3) and has a slope of -4

Step 1) identify the slope, the slope is -4. Step 2) find the y-intercept. Substitute the slope and the coordinate of the given point in y=mx+b. Solve for b. Write slope intercept form= 3=-4(-1)+b. -1=b. Step 3) write an equation of the line. Write slope intercept form= y=-4x-1

Write an equation of the line that passes through (-3,-5) and is parallel to the line y=3x-1

Step 1) the slope is 3 Step 2) find the y intercept -5=3(-3)+b 4=b Step 3) write an equation y=3x+4

Write an equation for the linear function f with the values f(0)=5 and f(4)=17

Step 1) write f(0)=5 as (0,5) and f(4)=17 as (4,17) Step 2) calculate the slope of the line that passes through (0,5) and (4,17) m=17-5/4-0=12/4=3 Step 3) write an equation of the line. The line crosses the y-axis at (0,5) so the y-intercept is 5= y=3x+5. Answer is f(x)=3x+5

Find the zero of a function.

Substitute 0 for y in the equation of the best fitting line and solve for x. y=-0.02x+1.435. 0=-0.02x+1.435. X~72

Write an equation of (2,-4)

The y-coordinate of the given point -4. This means all the points of the line have a y-coordinate of -4. An equation of the line is y=-4.

Write an equation to model data

Write an equation using 2 points on the line use (2,20) and (8,42) find the slope: 11/3. Find the y-intercept use the point (2,20) 20=11/3(2)+b 38/3=b. An equation of the line of fit is y=11/3x+38/3

Write two equations in standard form that are equivalent to 2x-6y=4

Write one equation by multiplying each side by 2= 4x-12y=8. Write the other by multiplying each side by .5= x-3y=2

How to make a scatter plot?

X will represent the domain and y will represent the range. Treat them as ordered pairs and plot them as points.

formula for point slope form

y-y1=m(x-x1)

Slope=8, y-intercept= -7

y=8x+-7

Formula for slope-intercept form?

y=mx+b