Question

Write an equation in point-slope form of the line that passes through the given points. Then write the equation in slope-intercept form.

(2, 4), (-3, -6)

Answer 1

To find the equation of a line in point-slope form, use the formula y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope. We find the slope-intercept form y = 2x.

Step-by-step explanation:

To find the equation of a line in point-slope form, we use the formula:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line. Let's use the given points (2, 4) and (-3, -6) to find the equation:

Step 1: Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (2, 4) and (-3, -6), the slope is:

m = (-6 - 4) / (-3 - 2) = -10 / -5

= 2

Step 2: Substitute the slope and one of the given points into the point-slope form:

y - 4 = 2(x - 2)

Step 3: Simplify the equation to slope-intercept form (y = mx + b):

y - 4 = 2x - 4

y = 2x - 4 + 4

y = 2x