Answer:
y = [tex]\frac{3}{2}[/tex]x + [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
The base form of the slope-intercept form is y = mx + b. We need to think of this as a system of linear equations problem, where we are solving for m and x using 2 equations. Substituting the x and y coordinates of the 2 points, we have 5 = m + b and -1 = -3m + b.
Let's now solve the system by elimination. We first subtract to eliminate the variable b and we get 6 = 4m, so m = [tex]\frac{3}{2}[/tex]. Then we substitute [tex]\frac{3}{2}[/tex] for m in any of the equations and we get b = [tex]\frac{7}{2}[/tex]. Thus, the equation of the line that goes through (1, 5) and (-3, -1) is y = [tex]\frac{3}{2}[/tex]x + [tex]\frac{7}{2}[/tex].
