Question

What is the equation of the line that passes through the point (5,8) and has a slope
of 3/5?

Answer 1

`y=(3)/(5)x+5`

Explanation:

The equation for a line in slope-intercept form is:

`y=mx+b`

Let's go through what each variable represents:

"y": y-coordinate for any point on the line

"m": slope of the line

"x": x-coordinate for any point on the line

"b": y-intercept (where the line intercepts the y-axis; represented by only the y-coordinate since the x-coordinate is 0)

Given:

Slope = 3/5

Passes through point (5, 8) --> x = 5, y = 8

Find:

y-intercept

We have determined what the question has given us, and what we need to find. Now, we can substitute the given values into the equation:

`y=mx+b\\8=(3)/(5)(5)+b\\8=(15)/(5)+b\\8=3+b\\$Subtract 3 from both sides\\$b=5`

Therefore the equation of the line is:

`y=(3)/(5)x+5`