Question

what is an equation of the line that passes through the points (-4, -7) and (2, 8)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1=-4,y_1 = - 7,x_2=2,y_2 = 8 \). So \( m=\frac{8-(-7)}{2-(-4)}=\frac{8 + 7}{2 + 4}=\frac{15}{6}=\frac{5}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \( (2,8) \). Substitute \( m = \frac{5}{2},x_1 = 2,y_1=8 \) into the formula: \( y - 8=\frac{5}{2}(x - 2) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-8=\frac{5}{2}x-5 \). Then add 8 to both sides: \( y=\frac{5}{2}x-5 + 8=\frac{5}{2}x+3 \). We can also write it in standard form. Multiply through by 2 to get \( 2y = 5x+6 \), or \( 5x-2y=-6 \). But the slope - intercept form \( y=\frac{5}{2}x + 3 \) is also a valid equation of the line.

Answer:

\( y=\frac{5}{2}x + 3 \) (or other equivalent forms like \( 5x-2y=-6 \))