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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. i'll use the points (8, 3) and (5, 0) from the line in order to calculate the slope. (8, 3) can be my [tex]x_2[/tex] and [tex]y_2[/tex] and (5, 0) can be my [tex]x_1[/tex] and [tex]y_1[/tex].
first, i'm going to plug in my [tex]y_2[/tex] and [tex]y_1[/tex] values, which are the y-values from each of the coordinate pairs. since i picked (8, 3) for [tex]x_2[/tex] and [tex]y_2[/tex] and (5, 0) for [tex]x_1[/tex] and [tex]y_1[/tex], i will be plugging in 3 for [tex]y_2[/tex] and 0 for [tex]y_1[/tex].
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] ⇒ [tex]\frac{3-0}{x_2-x_1}[/tex]
then i'll plug in my [tex]x_2[/tex] and [tex]x_1[/tex] values, which will be 8 and 5.
[tex]\frac{3-0}{x_2-x_1}[/tex] ⇒ [tex]\frac{3-0}{8-5}[/tex]
now simplify by subtracting 0 from 3 and 5 from 8.
the slope is [tex]\frac{3}{3}[/tex], which simplifies to 1 because [tex]\frac{3}{3}[/tex] 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
