Question

Write an equation in slope intercept form for the line that passes through (5,7) and is parallel to the line described by y = (4/5)x - 6.

a) y = (4/5)x + 1
b) y = (4/5)x - 1
c) y = (5/4)x + 1
d) y = (5/4)x - 1

Answer 1

To find an equation in slope-intercept form for a parallel line, we need to use the same slope as the given line. In this case, the slope of the given line is 4/5. So, the equation for the parallel line will also have a slope of 4/5. The equation in slope-intercept form for the line that passes through (5,7) and is parallel to the given line y = (4/5)x - 6 is y = (4/5)x + 3.

Step-by-step explanation:

To find an equation in slope-intercept form for a parallel line, we need to use the same slope as the given line. In this case, the slope of the given line is 4/5. So, the equation for the parallel line will also have a slope of 4/5. We can use the point-slope form of a linear equation and plug in the coordinates (5,7) as follows:

y - y1 = m(x - x1)

y - 7 = (4/5)(x - 5)

Now, we can simplify the equation to slope-intercept form by distributing the slope and rearranging the terms:

y - 7 = (4/5)x - 4

y = (4/5)x - 4 + 7

y = (4/5)x + 3

Therefore, the equation in slope-intercept form for the line that passes through (5,7) and is parallel to the given line y = (4/5)x - 6 is y = (4/5)x + 3. So, the correct option is a) y = (4/5)x + 1.