Algebra 1
L.19 Write an equation for a parallel or perpendicular line 5 SH
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The equation of line $t$ is $y=-\frac{1}{7} x-2$. Parallel to line $t$ is line $u$, which passes through the point $(7,6)$. What is the equation of line $u$ ?

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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Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：The slope of a line parallel to another line is the same as the slope of the original line. Therefore, the slope of line \(u\) is the same as the slope of line \(t\), which is \(-\frac{1}{7}\).

Step 3 ：We know that line \(u\) passes through the point \((7,6)\). We can substitute these values into the equation \(y = mx + b\) to find the y-intercept \(b\).

Step 4 ：Substituting \(x = 7\), \(y = 6\), and \(m = -\frac{1}{7}\), we get: \(6 = -\frac{1}{7} * 7 + b\)

Step 5 ：Solving for \(b\), we get: \(b = 6 + 1 = 7\)

Step 6 ：Therefore, the equation of line \(u\) in slope-intercept form is \(\boxed{y = -\frac{1}{7}x + 7}\)