Respuesta :
The point-slope formula is
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of a line passing through the point (x₁, y₁).
Also, the slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, the line passes through points (4, -3) and (-2, 5). Thus, we have:
x₁ = 4
y₁ = -3
x₂ = -2
y₂ = 5
Then, the slope is
[tex]m=\frac{5-(-3)}{-2-4}=\frac{5+3}{-6}=\frac{8}{-6}=-\frac{4}{3}[/tex]And the equation in point-slope form is
[tex]y-(-3)=-\frac{4}{3}(x-4)[/tex]Now, we need to rewrite this equation in slope-intercept form. The slope-intercept equation of a line with slope m and y-intercept b is
[tex]y=mx+b[/tex]Thus, we need to isolate y on the left side of the equation to obtain the slope-intercept form, as follows:
[tex]\begin{gathered} y+3=-\frac{4}{3}x-\frac{4}{3}(-4)\text{ using the distributive property of multiplication over addition} \\ \\ y+3=-\frac{4}{3}x+\frac{16}{3} \\ \\ y+3-3=-\frac{4}{3}x+\frac{16}{3}-3 \\ \\ y=-\frac{4}{3}x+\frac{16}{3}-\frac{9}{3} \\ \\ y=-\frac{4}{3}x+\frac{7}{3} \end{gathered}[/tex]Therefore, the slope-intercept form of that linear equation is
[tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]