Math / Geometry

QuestionGraph the line with $y$ -intercept 4 and slope 2.

Studdy Solution

STEP 1

1. The line is in the slope-intercept form, $y = mx + b$ .
2. The $y$ -intercept is $b = 4$ .
3. The slope of the line is $m = 2$ .

STEP 2

1. Write the equation of the line.
2. Identify key points using the slope and $y$ -intercept.
3. Plot the points and draw the line.

STEP 3

Write the equation of the line using the slope-intercept form:
$y = mx + b$
Substitute the given slope and $y$ -intercept:
$y = 2x + 4$

STEP 4

Identify the $y$ -intercept point:
The $y$ -intercept is the point where the line crosses the $y$ -axis. This occurs when $x = 0$ .
$(0, 4)$
Use the slope to find another point:
The slope $m = 2$ means that for every 1 unit increase in $x$ , $y$ increases by 2 units. Starting from the $y$ -intercept $(0, 4)$ , move 1 unit to the right (increase $x$ by 1) and 2 units up (increase $y$ by 2) to find another point:
$(1, 6)$

STEP 5

Plot the points $(0, 4)$ and $(1, 6)$ on the coordinate plane.
Draw a straight line through these points to represent the equation $y = 2x + 4$ .
The graph of the line is now complete.

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