Question

What is the equation of the line in slope-intercept form that passes through point (4, 5) and is parallel to the line y = −2x − 2? Show all necessary steps.

Answer 1

Answer:

$y=-2x+13$

Step-by-step explanation:

Slope-intercept form of a linear equation:

$y=mx+b$

where:

• m is the slope
• b is the y-intercept

Given equation:

$y=-2x-2$

Therefore, comparing the given equation with the slope-intercept form:

• slope (m) = -2
• y-intercept (b) = -2

The slopes of parallel lines are equal.

Therefore, the slope of the new line is -2.

Substitute the given point (4, 5) and the slope m = -2 into the slope-intercept formula and solve for b:

$\implies y=mx+b$

$\implies 5=-2(4)+b$

$\implies 5=-8+b$

$\implies b=13$

Finally, substitute the found values of m and b into the formula to create the equation of the line that passes through the given point and is parallel to the given line:

$\implies y=-2x+13$

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