Graph the line with slope 3/4 passing through the point (4, -1).
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 (4, -1). We can use the point-slope form of a line to find the equation of the line, and then use that to graph the line.
Answer
The line passes through the points (4, -1) and (8, 2). Its equation is $y = \frac{3}{4}x - 4$.
Answer for screen readers
size(8cm);
import graph;
real f(real x) { return 3/4*x - 4; }
pair A = (4,-1);
pair B = (8,2);
draw(graph(f,-2,10),red);
dot(A);
dot(B);
label("$" + string(A) + "$", A, SE);
label("$" + string(B) + "$", B, N);
xaxis(-10,10,Arrows(4));
yaxis(-10,10,Arrows(4));
label("$x$", (10,0), E);
label("$y$", (0,10), N);
Steps to Solve
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Plot the given point Plot the point (4, -1) 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 you move to the right (increase in x), you move 3 units up (increase in y). Starting from (4, -1), move 4 units to the right to x = 8. Then move 3 units up to y = 2. This gives us the point (8, 2).
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Draw the line Draw a straight line through the two points (4, -1) and (8, 2).
size(8cm);
import graph;
real f(real x) { return 3/4*x - 4; }
pair A = (4,-1);
pair B = (8,2);
draw(graph(f,-2,10),red);
dot(A);
dot(B);
label("$" + string(A) + "$", A, SE);
label("$" + string(B) + "$", B, N);
xaxis(-10,10,Arrows(4));
yaxis(-10,10,Arrows(4));
label("$x$", (10,0), E);
label("$y$", (0,10), N);
More Information
The slope-intercept form of the line is $y = \frac{3}{4}x - 4$.
Tips
A common mistake is incorrectly applying the slope. Remember that slope is rise over run and to move up or down based on the sign of the numerator and to the right or left based on the sign of the denominator. Another common mistake is misplotting the original point.
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