Question

What is an equation of the line that passes through the point left bracket, minus, 4, comma, 0, right bracket(−4,0) and is parallel to the line 5, x, minus, 4, y, equals, 205x−4y=20?

Answer 1

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use the point-slope form of a linear equation. The equation of the line that passes through the point (-4, 0) and is parallel to 5x - 4y = 20 is y = (5/4)x + 5.

Step-by-step explanation:

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use the point-slope form of a linear equation. The given line has the equation 5x - 4y = 20, which can be rewritten in slope-intercept form as y = (5/4)x - 5. The slope of the given line is 5/4, so the slope of the line parallel to it is also 5/4.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point, (-4, 0), and m is the slope, we have y - 0 = (5/4)(x - (-4)). Simplifying this equation gives y = (5/4)x + 5. Therefore, the equation of the line parallel to 5x - 4y = 20 that passes through the point (-4, 0) is y = (5/4)x + 5.