# How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

Apr 13, 2018

color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"

color(green)(Slope = m = 1.15, "y-intercept " = 9.2

#### Explanation:

Equation of a line, knowing two points on it is given by

$\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

(x_1,y_1) = -2, 6.9), (x_2,y_2) = (-4, 4.6)

$\frac{y - 6.9}{4.6 - 6.9} = \frac{x + 2}{- 4 + 2}$

$\frac{y - 6.9}{-} 2.3 = \frac{x + 2}{-} 2$

$\left(y - 6.9\right) = \frac{2.3 \cdot \left(x + 2\right)}{2} , \text{ cross multiplying}$

$y = 1.15 \cdot \left(x + 2\right) + 6.9$

color(blue)(y = 1.15 x + 9.2 " is the slope - intercept form"

color(green)(Slope = m = 1.15, "y-intercept " = 9.2

Apr 13, 2018

$y = 1.15 x + 9.2$

#### Explanation:

Since this is a linear variation of the form $y = m x + b$, any change in $x$ will create a proportional change in $y$.
$\left(- 2\right) - \left(- 4\right) = 2$ and
$\left(6.9\right) - \left(4.6\right) = 2.3$ so
for every 2 changes in $x$, $y$ changes by 2.3.
Divide each side by 2, and 1 change in $x$ corresponds to 1.15 in $y$, therefore the slope ($m$) must be 1.15.
Now we have the equation $y = 1.15 x + b$
Before, we said our change in $x$ by 2 resulted in a change in $y$ of 2.3. Therefore, if we move over right 2 from $\left(- 2 , 6.9\right)$, we reach the point $\left(0 , 9.2\right)$. Since the $x$-value is 0, this is the y-intercept ($b$)
The equation is $y = 1.15 x + 9.2$