Questions: Graph the line with slope 3 passing through the point (-3,-5).

Transcript text: Graph the line with slope 3 passing through the point $(-3,-5)$.

Solution

Solution Steps

Step 1: Given a point and slope

Given a point $(x_1, y_1) = (-3, -5)$ and a slope $m = 3$.

Step 2: Use the point-slope form to find the y-intercept

The point-slope form of a line equation is $y - y_1 = m(x - x_1)$. Substituting the given values, we get $y + 5 = 3(x + 3)$. Rearranging to slope-intercept form $y = mx + b$, we find the y-intercept $b$. $b = y_1 - m\cdot x_1 = -5 - 3\cdot-3 = 4$.

Step 3: Graphing the line

With the slope $m = 3$ and the y-intercept $b = 4$, the equation of the line is $y = 3x + 4$. To graph the line, plot the y-intercept on the y-axis. Then, use the slope to find another point on the line. Draw a straight line through these points to complete the graph.