Question

draw the line with the given intercepts.

1. x - intercept: 4

y - intercept: - 2

1. x - intercept: - 3

y - intercept: 1

1. x - intercept: - 2

y - intercept: - 4

1. x - intercept: 5

y - intercept: 2

1. x - intercept: $\frac{1}{2}$

y - intercept: - 3

1. x - intercept: 2

y - intercept: - $\frac{3}{2}$
graph the equation.

1. y = 2x + 1
2. y = - 6x + 4
3. y = 3x - 1
4. y = - x + 1
5. y = 3x
6. y = - 2x

Explanation:

Step1: Recall line - plotting using intercepts

To draw a line given $x$-intercept $a$ and $y$-intercept $b$, plot the points $(a,0)$ and $(0,b)$ and draw a straight - line through them.
For example, for problem 16 with $x$-intercept $a = 4$ and $y$-intercept $b=-2$, plot the points $(4,0)$ and $(0, - 2)$ and draw a line through them.
For problems 22 - 27 which are in the form $y=mx + c$ (slope - intercept form where $m$ is the slope and $c$ is the $y$-intercept):

Step2: Find two points for slope - intercept form

For the equation $y = mx + c$, first, the $y$-intercept is the point $(0,c)$. To find another point, we can set $x = 1$.
For $y=2x + 1$ (problem 22):
The $y$-intercept is $(0,1)$. When $x = 1$, $y=2\times1+1=3$, so another point is $(1,3)$. Plot these two points and draw a line.
For $y=-6x + 4$ (problem 23):
The $y$-intercept is $(0,4)$. When $x = 1$, $y=-6\times1 + 4=-2$, so another point is $(1,-2)$. Plot these two points and draw a line.
For $y = 3x-1$ (problem 24):
The $y$-intercept is $(0,-1)$. When $x = 1$, $y=3\times1-1 = 2$, so another point is $(1,2)$. Plot these two points and draw a line.
For $y=-x + 1$ (problem 25):
The $y$-intercept is $(0,1)$. When $x = 1$, $y=-1\times1 + 1=0$, so another point is $(1,0)$. Plot these two points and draw a line.
For $y = 3x$ (problem 26), the $y$-intercept is $(0,0)$. When $x = 1$, $y=3\times1=3$, so another point is $(1,3)$. Plot these two points and draw a line.
For $y=-2x$ (problem 27), the $y$-intercept is $(0,0)$. When $x = 1$, $y=-2\times1=-2$, so another point is $(1,-2)$. Plot these two points and draw a line.

There is no single numerical answer for this set of graph - drawing problems. The task is to graph the lines as described above. Each line is drawn by plotting the appropriate points and connecting them with a straight line.

Answer:

Step1: Recall line - plotting using intercepts

To draw a line given $x$-intercept $a$ and $y$-intercept $b$, plot the points $(a,0)$ and $(0,b)$ and draw a straight - line through them.
For example, for problem 16 with $x$-intercept $a = 4$ and $y$-intercept $b=-2$, plot the points $(4,0)$ and $(0, - 2)$ and draw a line through them.
For problems 22 - 27 which are in the form $y=mx + c$ (slope - intercept form where $m$ is the slope and $c$ is the $y$-intercept):

Step2: Find two points for slope - intercept form

For the equation $y = mx + c$, first, the $y$-intercept is the point $(0,c)$. To find another point, we can set $x = 1$.
For $y=2x + 1$ (problem 22):
The $y$-intercept is $(0,1)$. When $x = 1$, $y=2\times1+1=3$, so another point is $(1,3)$. Plot these two points and draw a line.
For $y=-6x + 4$ (problem 23):
The $y$-intercept is $(0,4)$. When $x = 1$, $y=-6\times1 + 4=-2$, so another point is $(1,-2)$. Plot these two points and draw a line.
For $y = 3x-1$ (problem 24):
The $y$-intercept is $(0,-1)$. When $x = 1$, $y=3\times1-1 = 2$, so another point is $(1,2)$. Plot these two points and draw a line.
For $y=-x + 1$ (problem 25):
The $y$-intercept is $(0,1)$. When $x = 1$, $y=-1\times1 + 1=0$, so another point is $(1,0)$. Plot these two points and draw a line.
For $y = 3x$ (problem 26), the $y$-intercept is $(0,0)$. When $x = 1$, $y=3\times1=3$, so another point is $(1,3)$. Plot these two points and draw a line.
For $y=-2x$ (problem 27), the $y$-intercept is $(0,0)$. When $x = 1$, $y=-2\times1=-2$, so another point is $(1,-2)$. Plot these two points and draw a line.

There is no single numerical answer for this set of graph - drawing problems. The task is to graph the lines as described above. Each line is drawn by plotting the appropriate points and connecting them with a straight line.