What is the equation of the line that passes through the points (-3,4) and (-6,3)? Write the answer in slope-intercept form.
To find the equation, we first need to find the slope of the line. The slope can be found by using the formula:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the given points.
Using \((x_1, y_1) = (-3, 4)\) and \((x_2, y_2) = (-6, 3)\), we can plug in the values:
\[m = \frac{{3 - 4}}{{-6 - (-3)}}\]
\[= \frac{{-1}}{{-3}}\]
\[= \frac{1}{3}\]
So, the slope of the line is \(m = \frac{1}{3}\).
Next, we use the point-slope form of the equation to find the equation of the line:
\[y - y_1 = m(x - x_1)\]
Plugging in \((x_1, y_1) = (-3, 4)\) and \(m = \frac{1}{3}\), we get:
\[y - 4 = \frac{1}{3}(x - (-3))\]
\[y - 4 = \frac{1}{3}(x + 3)\]
Finally, we can rewrite the equation in slope-intercept form \(y = mx + b\), where \(m = \frac{1}{3}\) and \(b\) is the y-intercept:
\[y - 4 = \frac{1}{3}x + 1\]
\[y = \frac{1}{3}x + 5\]
Therefore, the equation of the line that passes through the points (-3,4) and (-6,3) in slope-intercept form is \(y = \frac{1}{3}x + 5\).