Answer:
[tex]y=\frac{7}{4}x-9[/tex]
Step-by-step explanation:
Question:
Find the equation of the line through the point (4, -2) with slope [tex]\frac{7}{4}[/tex]
Answer + Step-by-step explanation:
Answer: [tex]y=\frac{7}{4}x-9[/tex]
Step-by-step explanation:
When trying to find the equation of a line passing through a point and then given the slope, always remember if you're trying to write the equation in slope-intercept form, find the slope and the y-intercept of the equation.
Slope-Intercept form: y = mx + b where m = slope and b = y-intercept
so the slope is already given but we have to find the y-intercept.
so... the equation of the line with a slope of [tex]\frac{7}{4}[/tex] is:
[tex]y=\frac{7}{4}x[/tex]
but in addition, we need a y-intercept so...
[tex]y=\frac{7}{4}x+b[/tex]
now use the given point on the question "(4, -2)" to solve for the y-intercept
so plug in the coordinates of the point in the equation:
[tex]y=\frac{7}{4}x+b[/tex]
[tex](-2)=\frac{7}{4}(4)+b[/tex]
[tex]-2=\frac{28}{4} +b[/tex]
[tex]-2=7+b[/tex]
[tex]b=-2-7[/tex]
[tex]b=-9[/tex]
so the y-intercept of the line is -9
and the equation of the line is [tex]y=\frac{7}{4}x-9[/tex]
