The equation for line g can be written as y+6=-(7)/(4)(x-6). Line h is parallel to line g and passes through (6,-7). 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.

Question

The equation for line  g can be written as  y+6=-(7)/(4)(x-6). Line  h is parallel to line  g and passes through  (6,-7). 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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Understand Relationship: Understand the relationship between lines g and h. Since line h is parallel to line g, they will have the same slope.Find Slope of Line g: Find the slope of line g. The equation of line g is given in point-slope form: y + 6 = -\frac{7}{4}(x - 6). The slope of line g is the coefficient of x, which is -\frac{7}{4}.Use Slope for Line h: Use the slope of line g for line h. Since line h is parallel to line g, the slope of line h is also -\frac{7}{4}.Find y-Intercept of Line h: Use the point (6, -7) to find the y-intercept of line h. We will use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Plug in the slope (-\frac{7}{4}) and the point (6, -7) into the equation to solve for b. -7 = -\frac{7}{4}(6) + b -7 = -\frac{42}{4} + b -7 = -\frac{21}{2} + b To find b, add \frac{21}{2} to both sides of the equation. b = -7 + \frac{21}{2} b = -\frac{14}{2} + \frac{21}{2} b = \frac{7}{2}Write Equation of Line h: Write the equation of line h in slope-intercept form. Now that we have the slope (-\frac{7}{4}) and the y-intercept (\frac{7}{2}), we can write the equation of line h. y = -\frac{7}{4}x + \frac{7}{2} To simplify the y-intercept to match the requested format, we convert \frac{7}{2} to quarters. \frac{7}{2} = \frac{14}{4} So the y-intercept in quarters is \frac{14}{4}, but we need to subtract \frac{7}{4}x from both sides to get the y-intercept alone. \frac{14}{4} - \frac{7}{4} = \frac{7}{4} Therefore, the y-intercept is \frac{7}{4}, and the equation of line h is: y = -\frac{7}{4}x + \frac{7}{4} However, we made a mistake in the calculation of the y-intercept. Let's correct it: b = -\frac{14}{2} + \frac{21}{2} b = \frac{7}{2} Converting to quarters: b = \frac{14}{4} So the correct y-intercept is \frac{14}{4}, which simplifies to \frac{7}{2}. The correct equation of line h is: y = -\frac{7}{4}x + \frac{7}{2} But we need to express the y-intercept as an improper fraction or integer. Since \frac{7}{2} is already in simplest form, we leave it as is. The final equation of line h is: y = -\frac{7}{4}x + \frac{7}{2}

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