To find the slope-intercept equation of a line, remember the general equation of a line in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Notice that the equation y=2x+4 is written in the slope-intercept form. Therefore, its slope is 2.
For two lines to be perpendicular, their slopes should have a product of -1.
Since we are looking for a line perpendicular to y=2x+4, the slope of the desired line should be -1/2.
[tex]m=-\frac{1}{2}[/tex]Use the point-slope formula to find the line with slope -1/2 that goes through the point (4,3):
[tex]y=m(x-x_0)+y_0[/tex]Substitute m=-1/2, x_0=4 and y_0=3:
[tex]y=-\frac{1}{2}(x-4)+3[/tex]To find the slope-intercept form of this equation, use the distributive property to rewrite -1/2 (x-4) as -1/2 x -(1/2)(-4):
[tex]y=-\frac{1}{2}x-\frac{1}{2}\cdot(-4)+3[/tex]Simplify the product (-1/2)(-4):
[tex]\begin{gathered} y=-\frac{1}{2}x+2+3 \\ \Rightarrow \\ y=-\frac{1}{2}x+5 \end{gathered}[/tex]Therefore, the slope intercept form of the equation of a line perpendicular to y=2x+4 and which goes through the point (4,3), is:
[tex]y=-\frac{1}{2}x+5[/tex]
