Answer:
The graph is in the attachment.
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - a point on a line
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
We have the equation in a point-slope form:
[tex]y+7=-\dfrac{4}{5}(x-4)[/tex]
[tex]y-(-7)=-\dfrac{4}{5}(x-4)[/tex]
Therefore we have one point: (4, -7).
Convert to the slope-intercept form:
[tex]y+7=-\dfrac{4}{5}(x-4)[/tex] use the distributive property
[tex]y+7=-\dfrac{4}{5}x+\left(-\dfrac{4}{5}\right)(-4)[/tex]
[tex]y+7=-\dfrac{4}{5}x+\dfrac{16}{5}[/tex]
[tex]y+7=-\dfrac{4}{5}x+3\dfrac{1}{5}[/tex] subtract 7 from both sides
[tex]y=-\dfrac{4}{5}x-3\dfrac{4}{5}[/tex]
Put x = -1 to the equation:
[tex]y=-\dfrac{4}{5}(-1)-3\dfrac{4}{5}=\dfrac{4}{5}-3\dfrac{4}{5}=-3[/tex]
Therefore we have the second point (-1, -3).
