Math

QuestionGraph the line with y-intercept 1 and slope 4.

Studdy Solution

STEP 1

Assumptions1. The y-intercept of the line is1. The slope of the line is43. We are graphing on a-dimensional Cartesian plane

STEP 2

The equation of a line in slope-intercept form is given byy=mx+by = mx + bwhere mm is the slope and bb is the y-intercept.

STEP 3

Substitute the given slope and y-intercept into the equation of the line.
y=x+1y =x +1

STEP 4

To graph the line, we start by plotting the y-intercept. The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is1, so we plot a point at (0,1).

STEP 5

The slope of the line is4, which is the ratio of the vertical change (rise) to the horizontal change (run). A slope of4 means that for every1 unit we move to the right on the x-axis, we move up4 units on the y-axis.

STEP 6

Starting from the y-intercept (0,1), move1 unit to the right and4 units up. Plot a point at this location (1,5).

STEP 7

Repeat the process of moving1 unit to the right and4 units up from the new point, and plot another point. Continue this process to plot several points.

STEP 8

Draw a straight line through the plotted points. This line represents the equation y=4x+1y =4x +1.
The graph of the line with y-intercept1 and slope4 has been drawn.

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