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The equation of line $g$ is $y=6x-7$ . Line $h$ , which is parallel to line $g$ , includes the point $(1,1)$ . What is the equation of line $h$ ? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Write an equation for a parallel or perpendicular line

Full solution

Q. The equation of line

g

is

y=6x-7

. Line

h

, which is parallel to line

g

, includes the point

(1,1)

. What is the equation of line

h

? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Identify parallel lines: Line $h$ is parallel to $g$ , so they have the same slope.
Determine point and slope: Line $h$ passes through the point $(1,1)$ and has the same slope as line $g$ , which is $6$ .
Use point-slope form: Plug the slope $6$ and the point $(1,1)$ into the equation $y=mx+b$ to find $b$ .
Isolate y-intercept: Solve for $b$ .
Calculate $b$ value: Subtract $6$ from both sides to isolate $b$ .
Write equation of line $h$ : Calculate the value of $b$ .
Write equation of line $h$ : Calculate the value of $b$ . Write the equation of line $h$ using the slope $6$ and y-intercept $-5$ .

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\newline

\newline

\text{(A)horizontal line}

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\newline

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Question

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