Aline goes through the points (8,9) and (-2,4). what is the slope of the line? (show your work) write the equation of the line in point-slope form. (show your work) write the equation of the line in slope-intercept form. (show your work)

Slope

The slope of the line between two points (x1, y1) and (x2, y2) is ...

... m = (y2 -y1)/(x2 -x1)

For your given points, the slope is

... m = (4 -9)/(-2 -8) = -5/-10

... m = 1/2

Equation

The point-slope form of the equation for a line can be written ...

... y = m(x -h) +k . . . . for a line of slope m through point (h, k)

Using the first point given and the slope just calculated, the equation for the line can be written ...

... y = (1/2)(x -8) +9

... y = (1/2)x -4 +9 . . . . eliminate parentheses; next, collect terms

... y = 1/2x +5

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

7

step-by-step explanation: