Write the equation of the line in slope-intercept form that passes through the points (0,2.3) , (5,−1.9) .(1 point) The equation in slope-intercept form is $$

1 answer

To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (0, 2.3) and (5, -1.9), we first need to determine the slope (m) of the line.

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points (0, 2.3) as \((x_1, y_1)\) and (5, -1.9) as \((x_2, y_2)\):

\[ m = \frac{-1.9 - 2.3}{5 - 0} \] \[ m = \frac{-4.2}{5} = -0.84 \]

Now that we know the slope \(m = -0.84\), we can use one of the points to find the y-intercept \(b\). Since one of the points is (0, 2.3), we see that the y-intercept \(b\) is directly the y-coordinate of this point, which is 2.3.

Now we can write the equation of the line in slope-intercept form:

\[ y = mx + b \] \[ y = -0.84x + 2.3 \]

Therefore, the equation of the line in slope-intercept form is: \[ \boxed{y = -0.84x + 2.3} \]