The two points will give the gradient of a straight line graph.
Consider the standard for of: y=mx+cy=mx+c
Where
yy is the answer
mm is the gradient (slope)
cc is the y-axis intercept (point where it crosses the y axis)
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color(brown)("Determine the gradient")Determine the gradient
Let point 1 ->P_1->(x_1,y_1) = (-8,-15)→P1→(x1,y1)=(−8,−15)
Let point 2 ->P_2->(x_2,y_2)=(-2,5)→P2→(x2,y2)=(−2,5)
The gradient (slope) is measured moving from left to right on the x-axis. As " " x_1 < x_2 " " x1<x2 (x_1" is less than "x_2x1 is less than x2) then we travel from P_1" to "P_2P1 to P2 for the gradient
So the gradient ->m=("change in up or down")/("change in along") larr "Left to right"→m=change in up or downchange in along←Left to right
m=("change in y-axis")/("change in x-axis") = (y_2-y_1)/(x_2-x_1)m=change in y-axischange in x-axis=y2−y1x2−x1
m=(5-(-15))/((-2)-(-8)) " "=" "20/6 = 10/3 color(red)( larr" Question answer")m=5−(−15)(−2)−(−8) = 206=103← Question answer
So the equation now is y=10/3x+cy=103x+c
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color(brown)("Determine y-intercept (crossing point on the y axis)")Determine y-intercept (crossing point on the y axis)
Using any one of the 2 given points substitute to solve for cc
P_1->(x_1,y_1)=(color(blue)(-8),color(green)(-15))P1→(x1,y1)=(−8,−15)
color(white)(.).
=>color(green)(y)=10/3color(blue)(x)+c" "->" "color(green)(-15)=10/3xx(color(blue)(-8))+c⇒y=103x+c → −15=103×(−8)+c
-15=-80/3+c−15=−803+c
Add 80/3803 to both sides
11 2/3 = c1123=c
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color(brown)("Putting it all together")Putting it all together
y=mx+c" "->" "y=10/3x+ 11 2/3y=mx+c → y=103x+1123
Note that 11 2/3 = 35/31123=353
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