Question

Write the equation of the line, in slope-intercept form, through the following points: -5,4 and -4,7

Answer 1

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

To find the slope(m), use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$    And plug in the two points on the line

(-5, 4) = (x₁, y₁)

(-4, 7) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{7-4}{-4-(-5)}$ (two negative signs cancel each other out and become positive)

$m=\frac{7-4}{-4+5}$

$m=\frac{3}{1}$

m = 3       Now that you know the slope, substitute/plug it into the equation:

y = mx + b

y = 3x + b    To find b, plug in either of the points into the equation, it doesn't matter which, then isolate/get the variable "b" by itself. I will use (-5, 4)

4 = 3(-5) + b

4 = -15 + b     Add 15 on both sides to get "b" by itself

4 + 15 = -15 + 15 + b

19 = b

y = 3x + 19