Question

Find the equation of the line parallel to y equals 1 half x plus 2 that passes through the point (4, 5) in slope-intercept form.

Answer 1

Answer: $y=\frac{1}{2}x+3$

Step-by-step explanation:

We can solve this by using the point-slope form, which can help get the equation of a line given the slope of the line and a point on the line. Slope-intercept form is the form $y=mx+b$, and we can convert from point-slope form to this with simple algebra.

The point-slope form is $y-y_1=m(x-x_1)$, where m is the slope of the line, and $(x_1,y_1)$ is the point.

We know that the line is parallel to $y=\frac{1}{2}x+2$, which means it will have the same slope. The slope of this line is $\frac{1}{2}$, so the slope of any line parallel to it will also be $\frac{1}{2}$.

$y-5=\frac{1}{2}(x-4)\\y-5=\frac{1}{2}x-2\\y=\frac{1}{2}x+3$