A line passes through the points (–3, –4) and (6, 2). What is the x-intercept of this line? Can someone please help I'm so confused

Given the points:

(–3, –4) and (6, 2)

x1 = -3

x2 = -4

y1 =6

y2 = 2

Determine the x-intercept of the line.

Solution:

Before finding the x-intercept of the line, we must first find the slope, the formula for point-slope form, and slope-intercept form.

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

Point-slope form: = (y - y1) = m(x -x1)

Slope-intercept form, y= mx+b

We start first by finding the slope.

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

m = -4/ -1

m = 4

Point-slope form: = (y - y1) = m(x -x1)

 ( y - 6) = 4 (x  + 3)

Point slope form: y - 6 = 4x + 12

To change into slope intercept form, we transpose -6 on the other side of the equation, note that when transposing a number, the sign changes.

y = 4x + 12 

Point slope form: y = 4x + 16

To find for the x intercept, substitute the value of x1 on the point slope form.

y = 4x +  16

y = 4(-3) + 16

y = -12 + 16

y = 4

Final answer:

X-intercept: y =4