Question

i can write a linear equation in slope-intercept form. hint: $y = mx + b$

1. slope = $\frac{7}{5}$, y-intercept = $-4$
2. slope = 3, y-intercept = 2

3)
4)

1. $4x - 5y = -10$
2. $x + 4y = -12$

i can write slope-intercept form given two points. (one point is the y-intercept.)

1. through: $(1, 2)$ and $(0, 3)$
2. through: $(-2, 5)$ and $(0, 4)$
3. through: $f(0)=3$ and $f(4)=2$
4. through: $f(0)=4$ and $f(2)=3$

Explanation:

Step1: Use slope-intercept formula

For problem 1: Substitute $m=\frac{7}{5}$, $b=-4$ into $y=mx+b$
$y=\frac{7}{5}x - 4$

Step2: Use slope-intercept formula

For problem 2: Substitute $m=3$, $b=2$ into $y=mx+b$
$y=3x + 2$

Step3: Identify $m$ and $b$ from graph

For problem 3: Slope $m=2$, y-intercept $b=-4$
$y=2x - 4$

Step4: Identify $m$ and $b$ from graph

For problem 4: Slope $m=-\frac{1}{2}$, y-intercept $b=2$
$y=-\frac{1}{2}x + 2$

Step5: Rearrange to slope-intercept form

For problem 5: Isolate $y$ from $4x-5y=-10$
$-5y=-4x-10 \implies y=\frac{4}{5}x + 2$

Step6: Rearrange to slope-intercept form

For problem 6: Isolate $y$ from $x+4y=-12$
$4y=-x-12 \implies y=-\frac{1}{4}x - 3$

Step7: Find $m$ and use $b$

For problem 7: $b=3$, $m=\frac{2-3}{1-0}=-1$
$y=-x + 3$

Step8: Find $m$ and use $b$

For problem 8: $b=4$, $m=\frac{5-4}{-2-0}=-\frac{1}{2}$
$y=-\frac{1}{2}x + 4$

Step9: Find $m$ and use $b$

For problem 9: $b=3$, $m=\frac{2-3}{4-0}=-\frac{1}{4}$
$y=-\frac{1}{4}x + 3$

Step10: Find $m$ and use $b$

For problem 10: $b=4$, $m=\frac{3-4}{2-0}=-\frac{1}{2}$
$y=-\frac{1}{2}x + 4$

Answer:

1. $y=\frac{7}{5}x - 4$
2. $y=3x + 2$
3. $y=2x - 4$
4. $y=-\frac{1}{2}x + 2$
5. $y=\frac{4}{5}x + 2$
6. $y=-\frac{1}{4}x - 3$
7. $y=-x + 3$
8. $y=-\frac{1}{2}x + 4$
9. $y=-\frac{1}{4}x + 3$
10. $y=-\frac{1}{2}x + 4$