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

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 = 4/5 x + 5.

∴ Required equation will be y = 4/5 x + k, since this line passes through C(-3, 8)

∴ 8 = [(4/5) ×(-3)] + k

40 = -12 + 5k

5k = 52

k = 52/5

∴ Required equation is y = 4/5 x + 52/5.

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

Aliter

Given equation of line is y = 4/5x + 5

5y = 4x + 25

4x - 5y + 25 = 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 = 4, B = -5 and (x₁, y₁) = (-3, 8)

∴ Required equation is 4(x + 3) - 5(y - 8) = 0

4x + 12 - 5y + 40 = 0

4x - 5y + 52 = 0

This is the equation in general form.

∴ Required equation is y = 4/5 x + 52/5 in the slope-intercept form.

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

Summary:

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