Answer:
a. gradient: 2/7
b. y -5 = 2/7(x +3)
Step-by-step explanation:
a.
The gradient of the line is found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (7 -5)/(4 -(-3)) = 2/7 . . . gradient of line AB
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b.
The equation of the line can be written in point-slope form as ...
y -k = m(x -h) . . . . . . line with gradient m through point (h, k)
Using point 'a' and the above gradient in the equation, the line is described by ...
y -5 = 2/7(x +3) . . . equation of AB
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Additional comment
The equation of the line can be written in several other forms. Eliminating parentheses and adding 5, we get slope-intercept form:
y = 2/7x +5 6/7
This can be rearranged to standard form
2x -7y = -41
Dividing by -41 puts the equation in intercept form:
x/(-41/2) +y/(41/7) = 1
Then your values of m and n are seen to be -41/2 and 41/7, respectively. These are highlighted on the attached graph.
