Answer
$y=x-1$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
(2) The slope of a line can be found using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line.
Solve for the slope to obtain:
$m=\dfrac{3-(-2)}{4-(-1)}
\\m=\dfrac{3+2}{4+1}
\\m=\dfrac{5}{5}
\\m=1$
Thus, the tentative equation of the line is:
$y=1(x)+b
\\y=x+b$
To find the value of $b$, substitute the coordinates of $(4, 3)$ into the tentative equation above to obtain:
$y=x+b
\\3 = 4+ b
\\3-4 = b
\\-1=b$
Therefore, the equation of the line is:
$y=x+(-1)
\\y=x-1$
