Question

Write the equation of a line that is parallel to {y=-\dfrac{5}{4}x+7}y=− 4 5 ​ x+7y, equals, minus, start fraction, 5, divided by, 4, end fraction, x, plus, 7 and that passes through the point {(-4,1)}(−4,1)left parenthesis, minus, 4, comma, 1, right parenthesis.

Answer 1

Write the equation of a line that is parallel to y=-5/4x + 7

Any line parallel to the given line will have the same slope. In an equation presented in the y-intercept form, the slope is always the coefficient of "x". In this case, the slope is -5/4 (meaning the next point is down 5, and 4 to the right).

Our equation so far looks like this: y = -5/4x + b

"b" represents the y-intercept. To solve for be, we will need to substitute values into x and y. The next piece of information it gives us is one of the points, or solutions, of the line. This means that since this point is on the line, we can use its x and y values to substitute.

x = -4

y= 1

y = -5/4x + b

1 = -5/4(-4) + b

1 = 5 + b

-4 = b

Final Answer: y = -(5/4)x -4