Math

QuestionFind the slope-intercept form of a line that passes through (5,3)(5,-3) with a slope of -4.

Studdy Solution

STEP 1

Assumptions1. The line passes through the point (5, -3) . The slope of the line is -43. We want to find the equation of the line in slope-intercept form, which is y=mx+by = mx + b, where m is the slope and b is the y-intercept.

STEP 2

We know the slope (m) of the line and a point (x, y) on the line. We can substitute these values into the slope-intercept form of the line equation, y=mx+by = mx + b, to solve for the y-intercept (b).
=45+b- = -4 \cdot5 + b

STEP 3

implify the equation to solve for b.
3=20+b-3 = -20 + b

STEP 4

Rearrange the equation to isolate b on one side.
b=3+20b = -3 +20

STEP 5

Calculate the value of b.
b=17b =17

STEP 6

Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line in slope-intercept form, y=mx+by = mx + b.
y=4x+17y = -4x +17The equation of the line that passes through the point (5, -3) and has a slope of -4 is y=4x+17y = -4x +17.

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