Question

$y=mx+b$

1. $y=-\frac{2}{3}x-1$
2. $y=-x-1$
3. $y=-2x-4$
4. $y=-\frac{1}{2}x-1$
5. $x=1$
6. $y=2$

directions: write the slope-intercept form of the equation with the given information.

1. slope $=\frac{7}{3}$, y-intercept $=-3$
2. through $(0, -1)$, slope $=\frac{1}{2}$
3. through $(4, 3)$, slope $=2$
4. through $(3, 4)$ and $(5, -2)$

Explanation:

Step1: Graph 4: Identify slope & intercept

Equation: $y=-\frac{2}{3}x - 1$
Slope $m=-\frac{2}{3}$, y-intercept $(0, -1)$
Plot $(0,-1)$, then move 2 down, 3 right to $(3,-3)$; draw line through points.

Step2: Graph 5: Identify slope & intercept

Equation: $y=-x - 1$
Slope $m=-1$, y-intercept $(0, -1)$
Plot $(0,-1)$, then move 1 down, 1 right to $(1,-2)$; draw line through points.

Step3: Graph 6: Identify slope & intercept

Equation: $y=-2x - 4$
Slope $m=-2$, y-intercept $(0, -4)$
Plot $(0,-4)$, then move 2 down, 1 right to $(1,-6)$; draw line through points.

Step4: Graph 7: Identify slope & intercept

Equation: $y=-\frac{1}{2}x - 1$
Slope $m=-\frac{1}{2}$, y-intercept $(0, -1)$
Plot $(0,-1)$, then move 1 down, 2 right to $(2,-2)$; draw line through points.

Step5: Graph 8: Plot vertical line

Equation: $x=1$
Draw a vertical line passing through $(1, y)$ for all $y$.

Step6: Graph 9: Plot horizontal line

Equation: $y=2$
Draw a horizontal line passing through $(x, 2)$ for all $x$.

Step7: Problem10: Use slope-intercept form

Slope $m=\frac{7}{3}$, y-intercept $b=-3$
Substitute into $y=mx+b$: $y=\frac{7}{3}x - 3$

Step8: Problem11: Use point-slope then simplify

Point $(0,-1)$, slope $m=\frac{1}{2}$
Point-slope: $y - (-1)=\frac{1}{2}(x-0)$
Simplify: $y+1=\frac{1}{2}x \implies y=\frac{1}{2}x -1$

Step9: Problem12: Solve for y-intercept

Point $(4,3)$, slope $m=2$
Substitute into $y=mx+b$: $3=2(4)+b$
Solve for $b$: $b=3-8=-5$
Equation: $y=2x -5$

Step10: Problem13: Calculate slope then intercept

Points $(3,4)$ and $(5,-2)$
Slope: $m=\frac{-2-4}{5-3}=\frac{-6}{2}=-3$
Substitute $(3,4)$ into $y=mx+b$: $4=-3(3)+b$
Solve for $b$: $b=4+9=13$
Equation: $y=-3x +13$

Answer:

Graphs:

1. Line through $(0,-1)$ and $(3,-3)$
2. Line through $(0,-1)$ and $(1,-2)$
3. Line through $(0,-4)$ and $(1,-6)$
4. Line through $(0,-1)$ and $(2,-2)$
5. Vertical line at $x=1$
6. Horizontal line at $y=2$

Equations:

1. $y=\frac{7}{3}x - 3$
2. $y=\frac{1}{2}x - 1$
3. $y=2x - 5$
4. $y=-3x + 13$