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. The slope is ¾ and the point is (-5, -4). We can start by plotting the point, then use the slope to find another point on the line, and finally draw the line through these two points.
Answer
The line passes through $(-5, -4)$ and has a slope of $\frac{3}{4}$.
Answer for screen readers
size(8cm);
import graph;
real f(real x) { return 3/4*x - 1/4; }
pair A = (-5,-4);
pair B = (-1,-1);
draw(graph(f,-10,10),red);
dot(A);
dot(B);
label("$(-5, -4)$", A, SW);
label("$(-1, -1)$", B, NE);
xaxis("$x$",-10,10,arrow=Arrow);
yaxis("$y$",-10,10,arrow=Arrow);
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 given as $\frac{3}{4}$. This means for every 4 units we move to the right on the x-axis, we move 3 units up on the y-axis. Starting from the point (-5, -4), move 4 units to the right (horizontally) and 3 units up (vertically). $$ (-5 + 4, -4 + 3) = (-1, -1)$$ So, another point on the line is (-1, -1).
- Draw the line
Draw a straight line passing through the points (-5, -4) and (-1, -1).
size(8cm);
import graph;
real f(real x) { return 3/4*x - 1/4; }
pair A = (-5,-4);
pair B = (-1,-1);
draw(graph(f,-10,10),red);
dot(A);
dot(B);
label("$(-5, -4)$", A, SW);
label("$(-1, -1)$", B, NE);
xaxis("$x$",-10,10,arrow=Arrow);
yaxis("$y$",-10,10,arrow=Arrow);
More Information
The line slopes upwards from left to right because it has a positive slope.
Tips
A common mistake is misinterpreting the slope. Remember, the slope $\frac{3}{4}$ means "rise over run," so for every 4 units you move to the right, you must move 3 units up. Another common mistake is to plot the point incorrectly.
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