Answer:
We conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
Given the line
y+2x=4
converting into the slope-intercept form y = mx+b where m is the slope
y = -2x+4
comparing with the slope-intercept form
Thus, the slope is: m = -2
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -2
The slope of the new line perpendicular to the given line = – 1/m
= -1/-2 = 1/2
Using the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 1/2 and the point (-3, 5)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-5=\frac{1}{2}\left(x-\left(-3\right)\right)[/tex]
[tex]y-5=\frac{1}{2}\left(x+3\right)[/tex]
Add 5 to both sides
[tex]y-5+5=\frac{1}{2}\left(x+3\right)+5[/tex]
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
Therefore, we conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
