Question

I watched a video and didn't get my free answer, can I have some help,

The slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?

y – 13 = 5(x – 2)
y + 13 = 5(x + 2)
y – 2 = 5(x – 13)
y + 2 = 5(x + 13)

Answer 1

y + 13 = 5(x + 2)

Explanation:

The slope-intercept form of the equation of a line is

y = mx + b,

where m = slope, and b = y-intercept.

From the slope-intercept equation y = 5x - 3, we see that the slope of the line is 3.

The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

where m = slope, and (x1, y1) is a point on the line.

We have point (-2, -13), so x1 = -2, and y1 = -13.

We also have slope 5, so m = 5.

Now we use the coordinates of the given point and the slope in the point-slope equation.

y - (-13) = 5(x - (-2))

We simplify to get

y + 13 = 5(x + 2)