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Math  /  Algebra

QuestionBOOKMARK CHECK ANSWER 呂 Q α\alpha ≡\equiv 8 CHLOEDON
Write the equation of a line that goes through the points (−5,6)(-5,6) and (10,−6)(10,-6). The final answer should be in Slope intercep

Studdy Solution

STEP 1

1. We are given two points: (−5,6)(-5, 6) and (10,−6)(10, -6).
2. We need to find the equation of the line in slope-intercept form, which is y=mx+by = mx + b.
3. The slope-intercept form requires finding the slope mm and the y-intercept bb.

STEP 2

1. Calculate the slope mm using the two points.
2. Use the slope and one of the points to solve for the y-intercept bb.
3. Write the equation of the line in slope-intercept form.

STEP 3

Calculate the slope mm using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (−5,6)(-5, 6) and (10,−6)(10, -6):
m=−6−610−(−5)=−1215=−45 m = \frac{-6 - 6}{10 - (-5)} = \frac{-12}{15} = -\frac{4}{5}

STEP 4

Use the slope m=−45m = -\frac{4}{5} and one of the points, say (−5,6)(-5, 6), to find the y-intercept bb.
Substitute into the slope-intercept form y=mx+by = mx + b:
6=−45(−5)+b 6 = -\frac{4}{5}(-5) + b
Simplify:
6=4+b 6 = 4 + b
Solve for bb:
b=6−4=2 b = 6 - 4 = 2

STEP 5

Write the equation of the line using the slope mm and y-intercept bb:
y=−45x+2 y = -\frac{4}{5}x + 2
The equation of the line is:
y=−45x+2 y = -\frac{4}{5}x + 2

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