Answer:
[tex]y = -\frac{5}{2} x + 3[/tex]
Step-by-step explanation:
We are given that a line passes through (-2, 8) and has a slope of -5/2.
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of this line, we can immediately plug it into the equation.
Replace m with -5/2.
[tex]y = -\frac{5}{2} x+ b[/tex]
Now we need to find b.
As the equation passes through the point (-2, 8), we can use its values to help solve for b.
Substitute -2 as x and 8 as y.
[tex]8 = -\frac{5}{2} (-2) +b[/tex]
Multiply.
8 = 5 + b
Subtract 5 from both sides.
3 = b
Replace b with 3 in the equation.
[tex]y = -\frac{5}{2} x + 3[/tex]
Topic: finding the equation of the line (slope-intercept form)
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