Write the equation of the line in the indicated form that meets each criterion below.
A. A line with a slope of -2/3 and a y-intercept of 4; in slope-intercept form
B. A line with a y-intercept of – 2 and an x-intercept of 3; in standard form
C. A line with a slope of – 3 and through the point (1, 2
A. y = -2x/3 + 4
B. goes through (0,-2) and (3,0)
(0+2)/(3-0) = 2/3 = (y+2)/(x-0)
y+2 = 2x/3
2x -3y = 6
C. y = -3 x + b
2 = -3(1) = b
b = 5
y = -3x + 5
A. Y = mx + b.
Y = (-2/3)X + 4.
B. ax + by = c.
(0,-2), (3,0).
m = (0-(-2))/(3-0) = 2/3.
Y = mx + b.
Y = (2/3)x - 2,
-2x/3 + y = -2,
Multiply both sides by -3:
2x -3y = 6. STD. form.
C. m = -3, P(1,2).
Y = mx + b.
2 = -3*1 + b, b = 5.
Eq: Y = -3x + 5.
To write the equation of a line in different forms, we need to use the slope (m) and either the y-intercept (b) or a point on the line (x1, y1).
A. The slope-intercept form of a line is y = mx + b. In this case, the slope (m) is -2/3 and the y-intercept (b) is 4. So, the equation of the line in slope-intercept form is y = (-2/3)x + 4.
B. The standard form of a line is Ax + By = C, where A, B, and C are constants. To find the values of A, B, and C, we can use the y-intercept (-2) and the x-intercept (3). The y-intercept gives us the point (0, -2), and the x-intercept gives us the point (3, 0).
First, we find the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1)
= (-2 - 0) / (0 - 3)
= -2 / (-3)
= 2/3.
Next, we use the slope-intercept form (y = mx + b) to find the y-intercept (b) using one of the points (0, -2):
-2 = (2/3)(0) + b
b = -2.
Therefore, the equation in slope-intercept form is y = (2/3)x - 2. Now, let's rewrite it in standard form:
Multiply the equation by 3 to eliminate the fraction:
3y = 2x - 6.
Rearrange terms to get:
2x - 3y = 6.
So, the equation of the line in standard form is 2x - 3y = 6.
C. With a slope of -3 and a point (1, 2), we can use the point-slope form of a line, which is y - y1 = m(x - x1). Plugging in the values, we have:
y - 2 = -3(x - 1).
Next, distribute -3 to the terms inside the parentheses:
y - 2 = -3x + 3.
Rearrange the terms to isolate y:
y = -3x + 5.
Thus, the equation of the line in slope-intercept form is y = -3x + 5.