The equation for the line in the graph given is 7x - 4y - 28 = 0. The points in the given graph are (0, -7) and (4, 0).
What is the equation of a line that passes through points?
Consider two points (x1, y1) and (x2, y2).
When a line passing through these points is calculated as
y - y1 = (y2 - y1)/(x2 - x1) × (x - x1)
Calculation:
The given line in the graph passes through the points (0, -7) and (4, 0). (By taking x = 0, we get y = -7 and y = 0, we get x = 4)
x1 = 0, x2 = 4, y1 = -7, y2 = 0
Then, the equation of the line is
y - y1 = (y2 - y1)/(x2 - x1) × (x - x1)
⇒ y + 7 = (0 + 7)/(4 - 0) × (x - 0)
⇒ y + 7 = 7/4 (x)
⇒ 4y + 28 = 7x
⇒ 7x - 4y - 28 = 0
Therefore, the equation of the given line in the graph is 7x - 4y - 28 = 0.
And the points that lie on the line are (0, -7) and (4, 0).
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