# Problem 938

Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation.

y = 5x + 2

Solution:-

Recall that the slope-intercept from of the equation of a nonvertical line with slopeĀ  m and y-intercept b is y = mx + b.

Notice that the equation y = 5x + 2 is already in the form y = mx + b.

The slope, m ,is the coefficient of x.

Therefore, the slope of the line whose equation is y = 5x + 2 is equal to 5.

The y-intercept, b, is the constant term. Therefore, the y-intercept of the line whose equation is y = 5x + 2 is equal to 2.

To graph the line, y = 5x + 2, begin by plotting the y-intercept. Plot the point (0,2) on the graph to the right.

Now , obtain a second point using the slope, m. Write m as a fraction, and use rise over run.

The slope is 5. We can write 5 as the fraction .

m =

Therefore, starting at the y-intercept, go up 5units and then to the right 1 unit. Plot this point on the graph to the right.

The line through two points is the graph of the equation.