What is the slope of the line passing through the points left-parenthesis 2 comma 7 right-parenthesis and left parenthesis negative 1 comma 3 right parenthesis?
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (2, 7) and (-1, 3):
slope = (3 - 7) / (-1 - 2)
= (-4) / (-3)
= 4/3
Therefore, the slope of the line passing through the points (2, 7) and (-1, 3) is 4/3.
The x-intercept of a line is negative 5 and the y-intercept of the line is negative 2. What is the equation of the line?
To find the equation of the line given the x-intercept and y-intercept, we can use the slope-intercept form of a straight line equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Since the x-intercept is -5 and the y-intercept is -2, we can plug these values into the equation to find the slope:
-2 = m * (-5)
-2 = -5m
Solving for m, we divide both sides by -5:
m = -2 / -5
m = 2/5
Now that we have the slope, we can substitute it in the slope-intercept form with the y-intercept (-2) to find the equation of the line:
y = (2/5)x - 2
Therefore, the equation of the line with an x-intercept of -5 and a y-intercept of -2 is y = (2/5)x - 2.
What is the slope-intercept form of the equation y minus 7 equals negative five-halves left parenthesis x plus 4 right parenthesis?
To rewrite the given equation in slope-intercept form (y = mx + b), we will first isolate y on one side:
Starting with:
y - 7 = -5/2 (x + 4)
Distribute -5/2 to the terms inside the parentheses:
y - 7 = (-5/2)x - 10
Now, add 7 to both sides to isolate y:
y = (-5/2)x - 10 + 7
Combine like terms:
y = (-5/2)x - 3
Therefore, the equation y - 7 = -5/2 (x + 4) can be written in slope-intercept form as y = (-5/2)x - 3.
What is the standard form of the equation y equals negative three-halves x plus 5?
To convert the equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), we can follow these steps:
Start with the given equation:
y = (-3/2)x + 5
Multiply all terms by 2 to eliminate the fraction:
2y = -3x + 10
Rearrange the terms to get the x and y terms on the same side:
3x + 2y = 10
Now, the equation is in standard form: 3x + 2y = 10.