Answer:
y = 1/4x +2
Step-by-step explanation:
The slope-intercept form of the equation for a line can be found by solving the given equation for y. It can be written directly from the slope and the y-intercept.
<h3>Solve for y</h3>
It is helpful to simplify the equation first, then isolate the y-variable by eliminating non-y terms from that side of the equation.
y -4 = (1/4)(x -8) . . . . . . . given
y -4 = (1/4)x -2 . . . . . . . . eliminate parentheses
y = 1/4x +2 . . . . . . . . . . add 4. This is the desired form
<h3>Use given information</h3>
Alternatively, you can use the given information to write the slope-intercept equation directly. The slope in the point-slope form is the multiplier outside parentheses. In y-4 = 1/4(x -8), the slope is 1/4.
The y-intercept is the point where the line crosses the y-axis. Its coordinates always have an x-coordinate of 0. That is, the given point (0, 2) tells you the y-intercept is 2.
Using the slope and intercept in the slope-intercept form, you get the equation you're looking for:
y = mx +b . . . . . line with slope m and y-intercept b
y = 1/4x +2 . . . . . line with slope 1/4 and y-intercept 2
