Question

Find the equation of the line Use exact numbers

Answer 1

Answer:

y = 1x + -5

Step-by-step explanation:

slope-intercept form is y = mx + b, where m = slope and b = y-intercept.

the line touches the y-axis at -5, therefore the y-intercept, or b, is -5.

y = mx + b ⇒ y = mx - 5

now i'll find the slope by picking two points from the line and finding the change in y over the change in x, aka $\frac{y_2-y_1}{x_2-x_1}$. i'll use the points (8, 3) and (5, 0)  from the line in order to calculate the slope. (8, 3) can be my $x_2$ and $y_2$ and (5, 0) can be my $x_1$ and $y_1$.

first, i'm going to plug in my $y_2$ and $y_1$ values, which are the y-values from each of the coordinate pairs. since i picked (8, 3) for $x_2$ and $y_2$ and (5, 0) for $x_1$ and $y_1$, i will be plugging in 3 for $y_2$ and 0 for $y_1$.

$\frac{y_2-y_1}{x_2-x_1}$ ⇒ $\frac{3-0}{x_2-x_1}$

then i'll plug in my $x_2$ and $x_1$ values, which will be 8 and 5.

$\frac{3-0}{x_2-x_1}$ ⇒ $\frac{3-0}{8-5}$

now simplify by subtracting 0 from 3 and 5 from 8.

• 3 - 0 = 3

• 8 - 5 = 3

the slope is $\frac{3}{3}$, which simplifies to 1 because $\frac{3}{3}$ or  3 ÷ 3 = 1.

the slope-intercept form equation for this line is y = 1x + -5 (or just y = x - 5, but since it's a fill-in-the-blank problem, the 1 will show in front of the y and -5 will come after the + sign.)

i hope this helps! have a lovely day <3

Answer 2

The answer is y = x - 5

Sub in 0 to find the y intercept, and count rise over run to find the slope (1)