Question

writing equations for lines between two points practice 2
name: sean birmingham
write an equation for a line that passes through the given point and has the given slope. show all your work.

1. (0,2); m = -4; b = ______

equation= _______________

1. (0,7); m = 1; b = ______

equation= _______________

1. (-8, -5); m = $\frac{3}{4}$; b = ______

equation= _______________

1. (3, 0); m = $-\frac{2}{3}$; b = ______

equation= _______________
write an equation for a line that passes through the given points.

1. (0,1) and (3, -4); m = ____ b= ____

equation= _______________

1. (0, -5) and (-3, 3); m = ____ b= ____

equation= _______________

Explanation:

We use the slope-intercept form of a line: $y = mx + b$, where $m$ is slope, $b$ is y-intercept.

Step1: Find $b$ for (0,2), $m=-4$

Point (0,2) is the y-intercept, so $b=2$.
Equation: $y = -4x + 2$

Step2: Find $b$ for (0,7), $m=1.5$

Point (0,7) is the y-intercept, so $b=7$.
Equation: $y = 1.5x + 7$

Step3: Solve for $b$ with $(-8,-5), m=-\frac{3}{4}$

Substitute into $y=mx+b$: $-5 = -\frac{3}{4}(-8) + b$
$-5 = 6 + b \implies b = -11$
Equation: $y = -\frac{3}{4}x - 11$

Step4: Solve for $b$ with $(3,0), m=-\frac{2}{3}$

Substitute into $y=mx+b$: $0 = -\frac{2}{3}(3) + b$
$0 = -2 + b \implies b = 2$
Equation: $y = -\frac{2}{3}x + 2$

Step5: Calculate $m$, then $b$ for (0,1) & (3,-4)

Slope formula: $m = \frac{y_2-y_1}{x_2-x_1} = \frac{-4-1}{3-0} = -\frac{5}{3}$
Point (0,1) is y-intercept, so $b=1$.
Equation: $y = -\frac{5}{3}x + 1$

Step6: Calculate $m$, then $b$ for (0,-5) & (-3,3)

Slope formula: $m = \frac{3-(-5)}{-3-0} = \frac{8}{-3} = -\frac{8}{3}$
Point (0,-5) is y-intercept, so $b=-5$.
Equation: $y = -\frac{8}{3}x - 5$

Answer:

1. $b=2$; Equation: $y = -4x + 2$
2. $b=7$; Equation: $y = 1.5x + 7$
3. $b=-11$; Equation: $y = -\frac{3}{4}x - 11$
4. $b=2$; Equation: $y = -\frac{2}{3}x + 2$
5. $m=-\frac{5}{3}$, $b=1$; Equation: $y = -\frac{5}{3}x + 1$
6. $m=-\frac{8}{3}$, $b=-5$; Equation: $y = -\frac{8}{3}x - 5$