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 3/4 and the point is (-5, -4). We can use this information to plot the line on a graph.
Answer
The line passes through $(-5, -4)$ and has a slope of $\frac{3}{4}$.
Answer for screen readers
size(200);
import graph;
real f(real x) { return 3/4*x - 1/4; }
xaxis(-10, 10, Arrows(4));
yaxis(-10, 10, Arrows(4));
dot((-5,-4));
dot((-1,-1));
draw(graph(f,-10,10),red);
label("(-5,-4)", (-5,-4), SW);
label("(-1,-1)", (-1,-1), NE);
Steps to Solve
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Plot the given point Plot the point $(-5, -4)$ on the coordinate plane.
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Use the slope to find another point The slope is $\frac{3}{4}$, which 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 and 3 units up. This brings us to the point $(-5+4, -4+3) = (-1, -1)$.
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Draw the line Draw a straight line that passes through the points $(-5, -4)$ and $(-1, -1)$.
size(200);
import graph;
real f(real x) { return 3/4*x - 1/4; }
xaxis(-10, 10, Arrows(4));
yaxis(-10, 10, Arrows(4));
dot((-5,-4));
dot((-1,-1));
draw(graph(f,-10,10),red);
label("(-5,-4)", (-5,-4), SW);
label("(-1,-1)", (-1,-1), NE);
More Information
The graph of the line is a visual representation of all the points $(x, y)$ that satisfy the equation of the line. In this case, the equation of the line can be found using the point-slope form: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope. Substituting the given values, we have $y - (-4) = \frac{3}{4}(x - (-5))$, which simplifies to $y + 4 = \frac{3}{4}(x + 5)$. Further simplification leads to $y = \frac{3}{4}x + \frac{15}{4} - 4 = \frac{3}{4}x - \frac{1}{4}$.
Tips
A common mistake is misinterpreting the slope. For example, someone might move 3 units to the right and 4 units up, instead of 4 units to the right and 3 units up. Another mistake is making an arithmetic error when calculating the coordinates of the second point.
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