Answer:
An equation that represents the line is:
y = 3/4x - 9/2
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
Given the attached graph of a line.
Taking two points from the line, such as
Determining the slope between (2, -3) and (0, 6)
[tex]\left(x_1,\:y_1\right)=\left(2,\:-3\right),\:\left(x_2,\:y_2\right)=\left(6,\:0\right)[/tex]
[tex]m=\frac{0-\left(-3\right)}{6-2}[/tex]
refine
[tex]m=\frac{3}{4}[/tex]
substituting m = 3/4 and the point (2, -3) in the slope-intercept form of the line equation
y = mx + b
[tex]\left(-3\right)=\frac{3}{4}\left(2\right)+b[/tex]
[tex]\frac{3}{2}+b=-3[/tex]
subtract 3/2 from both sides
[tex]\frac{3}{2}+b-\frac{3}{2}=-3-\frac{3}{2}[/tex]
[tex]b=-\frac{9}{2}[/tex]
now substituting b = -9/2 and m = 3/4 in the slope-intercept form of the line equation
y = mx + b
y = 3/4x + (-9/2)
Therefore, an equation that represents the line is:
y = 3/4x - 9/2
