Graph the line with slope -3/4 passing through the point (-5, -4).
Understand the Problem
The question asks to graph a line given its slope and a point it passes through. This involves understanding the concept of slope and how to use it to find other points on the line, starting from the given point.
Answer
The line passes through the points $(-5, -4)$ and $(-1, -7)$.
Answer for screen readers
The line passes through the points $(-5, -4)$ and $(-1, -7)$.
Steps to Solve
-
Plot the given point. Plot the point $(-5, -4)$ on the coordinate plane.
-
Use the slope to find another point. The slope is $\frac{-3}{4}$. This means for every 4 units you move to the right (positive direction) on the x-axis, you move 3 units down (negative direction) on the y-axis. So, starting from $(-5, -4)$, move 4 units to the right and 3 units down. $x$-coordinate: $-5 + 4 = -1$ $y$-coordinate: $-4 - 3 = -7$ The new point is $(-1, -7)$.
-
Draw a line through the two points. Draw a straight line passing through the points $(-5, -4)$ and $(-1, -7)$. This line represents the equation with the given slope and passing through the given point.
The line passes through the points $(-5, -4)$ and $(-1, -7)$.
More Information
The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. You can also use the point-slope form of a line, $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line. In this case, $y - (-4) = -\frac{3}{4}(x - (-5))$, which simplifies to $y + 4 = -\frac{3}{4}(x + 5)$. Then $y = -\frac{3}{4}x - \frac{15}{4} - 4 \implies y = -\frac{3}{4}x - \frac{31}{4}$.
Tips
A common mistake is to misinterpret the negative slope. A slope of $-\frac{3}{4}$ means either "down 3, right 4" or "up 3, left 4". Moving in the wrong direction will result in an incorrect line. Another is not to perform the arithmetic correctly when using the slope to calculate a new point.
AI-generated content may contain errors. Please verify critical information
