Question

y = 3x - 2; y = 4x + 3; y = 6/5x + 1.5

Explanation:

Step1: Identify slope-intercept form

All equations use $y=mx+b$, where $m$=slope, $b$=y-intercept.

Step2: Find points for $y=3x-2$

• When $x=0$, $y=3(0)-2=-2$ → $(0,-2)$
• When $x=1$, $y=3(1)-2=1$ → $(1,1)$
• When $x=2$, $y=3(2)-2=4$ → $(2,4)$

Plot these points, draw a straight line.

Step3: Find points for $y=4x+3$

• When $x=0$, $y=4(0)+3=3$ → $(0,3)$
• When $x=1$, $y=4(1)+3=7$ → $(1,7)$
• When $x=-1$, $y=4(-1)+3=-1$ → $(-1,-1)$

Plot these points, draw a straight line.

Step4: Find points for $y=6/5x-3$ (rewritten)

• When $x=0$, $y=\frac{6}{5}(0)-3=-3$ → $(0,-3)$
• When $x=5$, $y=\frac{6}{5}(5)-3=3$ → $(5,3)$
• When $x=-5$, $y=\frac{6}{5}(-5)-3=-9$ → $(-5,-9)$

Plot these points, draw a straight line.

Step5: Find points for $x=5$

This is a vertical line. It passes through all points where $x=5$, e.g., $(5,0)$, $(5,4)$, $(5,-2)$. Draw a vertical line at $x=5$.

Answer:

1. For $y=3x-2$: Line through $(0,-2)$, $(1,1)$, $(2,4)$
2. For $y=4x+3$: Line through $(0,3)$, $(1,7)$, $(-1,-1)$
3. For $y=\frac{6}{5}x-3$: Line through $(0,-3)$, $(5,3)$, $(-5,-9)$
4. For $x=5$: Vertical line through $x=5$ (any $y$-value)
5. For the partially visible $y=3/5x+1$:

• When $x=0$, $y=1$ → $(0,1)$
• When $x=5$, $y=\frac{3}{5}(5)+1=4$ → $(5,4)$
• Line through these points

1. For the partially visible horizontal line: Assume $y=k$ (constant), e.g., if $y=4$, draw horizontal line through $(0,4)$, $(3,4)$