Answer:
1. x-intercept = (1, 0), y-intercept = (0, -2)
7. y + 4 = -6( x - 7)
Step-by-step explanation:
Question 1
Given point-slope equation:
[tex]y-2=2(x-2)[/tex]
The x-intercept is when y = 0:
[tex]\begin{aligned}y=0\implies 0-2 &=2(x-2)\\-2&=2x-4\\2&=2x\\x&=1\end{aligned}[/tex]
The y-intercept is when x = 0:
[tex]\begin{aligned}x=0\implies y-2 &=2(0-2)\\y-2&=2(-2)\\y-2&=-4\\y&=-2\end{aligned}[/tex]
Therefore, the intercepts are:
- x-intercept = (1, 0)
- y-intercept = (0, -2)
To graph the equation, plot the intercepts and draw a straight line through them. (See attachment 1).
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Question 7
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Given:
Substitute the given slope and point (7, -4) into the formula to write the equation of the line in point-slope form:
[tex]\implies y-(-4)=-6(x-7)[/tex]
[tex]\implies y+4=-6(x-7)[/tex]
To graph the line, find the value of y when x = 6 and when x = 8:
[tex]\begin{aligned}x=6\implies y+4 &=-6(6-7)\\y+4 &=-6(-1)\\y+4&=6\\y&=2\end{aligned}[/tex]
[tex]\begin{aligned}x=8\implies y+4 &=-6(8-7)\\y+4 &=-6(1)\\y+4&=-6\\y&=-10\end{aligned}[/tex]
To graph the equation, plot the points (6, 2) and (8, -10) and draw a straight line through them. (See attachment 2).
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Please note that I have drawn the graphs using the same size 7x7 grids as shown in your question paper. If you wish to graph more of the line, please change the scale from those I have used.
