Question

Find the equation of the line that is parallel to the line y=-2x-10 and passes through the point (1,-6) . Write the equation in slope-intercept form.

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Answer 1

line equation

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y = -2x - 10

gradient (m) = -2

bec the line is parallel to the line y = -2x - 10, so the gradients of them are same.

y - y1 = m(x - x1)

y + 6 = -2 (x - 1)

y + 6 = -2x + 2

y = -2x - 4

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Answer 2

the equation of the line that is parallel to y = -2x - 10 and passes through the point (1,-6) is y = -2x - 4.

Explanation:

To find the equation of a line that is parallel to another line, we can use the slope of the given line. Since the given line is in slope-intercept form, we can find the slope by looking at the coefficient of the x term, which is -2. Therefore, the slope of the line is -2.

Since the line we are trying to find is parallel to the given line, it will also have a slope of -2. Therefore, the equation of the line we are trying to find can be written in the form y = -2x + b, where b is a constant.

We are also told that the line passes through the point (1,-6), which means that we can substitute these values into the equation to solve for b:

`y = -2x + b-6 = -2(1) + b-6 = -2 + b-6 - (-2) = b-4 = b`

Therefore, the equation of the line that is parallel to y = -2x - 10 and passes through the point (1,-6) is y = -2x - 4.