Question

Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2

Answer 1

The slope-intercept form is

$y=mx+b$

m is the slope

b is the y-intercept

The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is

$m=\frac{y2-y1}{x2-x1}$

From the given graph, the line passes through points (1, -4) and (0, 2)

Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)

$\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}$

Substitute the value of m in the form of the equation

$y=-6x+b$

Since the line intersects the y-axis at point (0, 2)

Then the y-intercept is 2

Then b = 2

The equation of the line is

$y=-6x+2$