Write an equation for the line parallel to the given line that contains C. C(-3,7); y = 8/9x + 7.

Solution:

We have an equation of line parallel to y = mx + c is of the form y= mx + k.

Given that the required line is parallel to y = 8/9 x + 7.

∴ Required equation will be y = 8/9 x + k, since this line passes through C(-3, 7)

∴ 7 = [(8/9) ×(-3)] + k

63 = -24 + 9k

9k = 87

k = 87/9

∴ Required equation is y = 8/9 x + 87/9 .

This equation of line is in the slope-intercept form.

Aliter

Given equation of line is y = 8/9x + 7

9y = 8x + 63

8x - 9y + 63 = 0

The above equation is in the general form of the equation of line .

Now, equation of a line parallel to Ax + By + C = 0 and passing through (x₁, y₁) is A(x - x₁) + B(y - y₁)=0

Here, A = 8, B = -9 and (x₁, y₁) = (-3, 7)

∴ Required equation is 8(x + 3) - 9(y - 7) = 0

8x + 24 - 9y + 63 = 0

8x - 9y + 87 = 0

This is the equation in general form.

Rewriting this in the slope-intercept form, we get y = 8/9 x + 87/9 .

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Write an equation for the line parallel to the given line that contains C. C(-3,7); y = 8/9x +7.

Summary:

The equation for the line parallel to the given line that contains C(-3,7); y = 8/9x+5, in slope intercept form is y = 4/5 x + 52/5.