Question

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 $$
.

Answer 1

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 need to calculate the slope (m) first.

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

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

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

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

Now that we have the slope \(m = -0.84\), we can use the point (0, 2.3) to find the y-intercept \(b\). Since the x-coordinate is 0 at this point, the y-coordinate is the y-intercept:

\[
b = 2.3
\]

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

\[
y = mx + b
\]

Substituting in the values we've found:

\[
y = -0.84x + 2.3
\]

So the equation in slope-intercept form is:

\[
\boxed{y = -0.84x + 2.3}
\]