1. What is the equation of the line that passes through (4,-1) and (-2,3)?
2. What is the equation of the line with an x-intercept of -1 and a y-intercept of 2?
To find the equation of a line, you can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
1. Given two points on the line: (4,-1) and (-2,3)
Step 1: Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1)
m = (3 - (-1)) / (-2 - 4) = 4 / (-6) = -2/3
Step 2: Choose one of the points, for example (4, -1), and substitute the values into the point-slope form equation:
y - y1 = m(x - x1)
y - (-1) = (-2/3)(x - 4)
y + 1 = (-2/3)(x - 4)
Step 3: Simplify the equation:
y + 1 = (-2/3)x + (8/3)
y = (-2/3)x + (8/3) - 1
y = (-2/3)x + (5/3)
Therefore, the equation of the line passing through (4,-1) and (-2,3) is y = (-2/3)x + (5/3).
2. Given x-intercept of -1 and y-intercept of 2.
The x-intercept is the point where the line intersects the x-axis, which occurs when y = 0, and the y-intercept is the point where the line intersects the y-axis, which occurs when x = 0.
Step 1: Substitute the x-intercept (-1, 0) into the point-slope form equation:
y - y1 = m(x - x1)
y - 0 = m(x - (-1))
y = m(x + 1)
Step 2: Substitute the y-intercept (0, 2) into the equation obtained above:
2 = m((0) + 1)
2 = m(1)
m = 2
Step 3: Substitute the slope (m) value into the equation:
y = 2(x + 1)
Therefore, the equation of the line with an x-intercept of -1 and a y-intercept of 2 is y = 2(x + 1).
1. The slope of that line is
m = (y2 - y1)/(x2 - x1) = 4/-6 = -2/3
Using y = mx + b standard format,
and the second data point valuesl
3 = (-2/3)*(-2) + b.
so b = 3 - 4/3 = 5/3
y = (-2/3)x +5/3
or
3y = 5 - 2x
2. When x=0, y = 2
When y = 0, x = -1
y = m x + 2
0 = m*(-1) +2
m = 2
y = 2x + 2
2nd question shortcut: or a straight line, use
x/(x-intercept) + y/(y-intercept) = 1
x/-1 + y/2 = 1
multiply each term by -2
2x - y = -2
done.