Answer:
Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct
I am simply providing an explanation in case you need it
Step-by-step explanation:
The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b
where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis
Given two points (x₁, y₁) and (x₂, y₂) on the straight line, we can compute the slope as follows
m = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]
Two distinct points on the line are at (0, -3) and (5,-4)
[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]
So we know the equation to be
[tex]y = - \frac{1}{5}x + b[/tex]
To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b
However, looking at the graph we see that the line crosses the y axis at
y = -3. So this is the value for the y intercept i.e. b
The equation of the line is therefore
[tex]y = - \frac{1}{5}x - 3[/tex]