Answer:
y=4x-16
Explanation:
The general form of the equation of a line is: y=mx+x, where m is the gradient and c is the y-intercept.
Given points (-3,-3) and (-1,5)
We are to find the equation of the line parallel to the given line with an x-intercept of 4.
First, we determine the value of the gradient of the line.
Gradient,
![m=\frac{y_2-y_1}{x_2-x_1} \\=\frac{5-(-3)}{-1-(-3)} \\=\frac{5+3}{-1+3}\\=\frac{8}{2}\\m=4](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%5C%5C%3D%5Cfrac%7B5-%28-3%29%7D%7B-1-%28-3%29%7D%20%5C%5C%3D%5Cfrac%7B5%2B3%7D%7B-1%2B3%7D%5C%5C%3D%5Cfrac%7B8%7D%7B2%7D%5C%5Cm%3D4)
Two lines are parallel if their gradients
are equal.
The gradient of the line parallel to the given line ![m_2=4](https://tex.z-dn.net/?f=m_2%3D4)
Since the x-intercept of the new line is 4, a point on the new line, ![(x_1,y_1)=(4,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%284%2C0%29)
Substituting
into the equation of a line: ,
we have:
![y-0=4(x-4)\\$Therefore:\\y=4x-16](https://tex.z-dn.net/?f=y-0%3D4%28x-4%29%5C%5C%24Therefore%3A%5C%5Cy%3D4x-16)
Therefore, the equation of the line is: y=4x-16