Exercise 19 Page 319

To write both the slope-intercept and the point-slope form equations, we need to find the slope of the line. To do so, we will substitute the given points into the Slope Formula.

Now, let's form our equations.

Point-Slope Form

Let's recall the general form of a point-slope equation. y- y_1= m(x- x_1) Here, m is the slope and ( x_1, y_1) is a point on the line. We already calculated the slope m= 32. We have also been given two points on the line. Since we only need one point to write the point-slope equation, let's use ( 1, 4). y- 4= 3/2(x- 1) Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!

Slope-Intercept Form

Let's recall the general form of a slope-intercept equation. y= mx+ b Here, m represents the slope and b represents the y-intercept. We already calculated the slope m= 32 above. The next step is substituting one of the points in the equation and then solving for the y-intercept b. Let's use the point ( 1, 4) one more time.

Now that we know the y-intercept is 52, we can write the slope-intercept form of the line. y=3/2x+ 5/2