What is the equation of the line that passes through the point (8,2) and has a slope of -3/4?

1 answer

To find the equation of the line that passes through a given point (x1, y1) = (8, 2) and has a slope m, you can use the point-slope form of a line's equation:

y - y1 = m(x - x1)

Given that the slope m = -3/4 and the point (8, 2) lies on the line, you can substitute these values into the formula:

y - 2 = (-3/4)(x - 8)

From here, you can either leave the equation in point-slope form, or you can rewrite it into slope-intercept form y = mx + b or standard form Ax + By = C.

Let's solve for the slope-intercept form:

y - 2 = (-3/4)(x - 8)

Multiply both sides to get rid of the fraction:

4(y - 2) = -3(x - 8)

Now distribute the 4 and -3 on both sides of the equation:

4y - 8 = -3x + 24

Next, you want to solve for y to get the equation in slope-intercept form:

4y = -3x + 24 + 8

4y = -3x + 32

Now, divide everything by 4 to solve for y:

y = (-3/4)x + 8

The slope-intercept form of the line that passes through the point (8, 2) with a slope of -3/4 is thus:

y = (-3/4)x + 8