4. y varies directly with x. When x = 8, y = 24. What is y when x = 10?
If you multiply 8 by 3, you get 24. Because you multiply x by 3 to get y, you can multiply 10 by 3, and you get 30
y is 30. (second option)
5. Slope intercept form is:
y = mx + b
"m" is the slope, "b" is the y-intercept
Since you know the slope is 2/3, and the y-intercept is 9, your equation is:
y = 2/3x + 9 (third option)
6. You want to find an equation in slope intercept form for the line that passes through the points (1 , -3) and (3 , 1)
y = mx + b
You need to find "m" and "b". To find the slope, you can use the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
And plug in the points (1, -3) and (3,1)
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{1-(-3)}{3-1} =\frac{1+3}{3-1} =\frac{4}{2} =2[/tex]
y = 2x + b
To find "b", you can plug in one of the points into the equation. I will plug in (3,1)
y = 2x + b
1 = 2(3) + b
1 = 6 + b
-5 = b
y = 2x - 5 (fourth choice)
