Question

A line passes through the point (-2,5) and has a slope of -6 write an equation in slope intercept form of this line

Answer 1

The slope-intercept form of the equation of a line has the following structure:

$y=mx+b$

Where m is the slope of the line, and b is the y-intercept. We already know that the slope of the line is -6, then:

$y=-6x+b$

To find b we can use the given point, whose x-coordinate is -2 and y-coordinate 5.

We can replace the values of x and y of the point and solve for b:

$\begin{gathered} 5=-6\cdot(-2)+b \\ \\ 5=12+b \\ \\ b=5-12 \\ \\ b=-7 \end{gathered}$

Now we know the value of the y-intercept. The equation if the line is:

$y=-6x-7$