Question

Find a general form of an equation of the line through the point A that satisfies the given condition.
A(6, −5); parallel to the line 7x − 4y = 8

Answer 1

Question:

Find a general form of an equation of the line through the point A that satisfies the given condition.

A(6, -5); parallel to the line 7x - 4y = 8

Answer:

To find the equation of a line parallel to the given line 7x - 4y = 8, we need to first determine the slope of the given line. The slope of a line is determined by the coefficients of x and y when the equation is in slope-intercept form (y = mx + b).

Let's rearrange the given equation 7x - 4y = 8 into slope-intercept form:

4y = 7x - 8
y = (7/4)x - 2

Now, we see that the slope of the given line is m = 7/4.

Since parallel lines have the same slope, the line parallel to 7x - 4y = 8 will also have a slope of 7/4.

Now, we have the slope m = 7/4 and the point A(6, -5).

We can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

Substitute x1 = 6, y1 = -5, and m = 7/4:

y - (-5) = (7/4)(x - 6)

Simplify:

y + 5 = (7/4)x - (7/4) * 6
y + 5 = (7/4)x - 42/4
y + 5 = (7/4)x - 10.5

Now, to express the equation in general form, move y to the left side:

y = (7/4)x - 10.5 - 5
y = (7/4)x - 15.5

So, the general form of the equation of the line through point A(6, -5) and parallel to the line 7x - 4y = 8 is y = (7/4)x - 15.5