Write the slope-intercept equation of the function f whose graph satisfies the given conditions.
The graph of f is perpendicular to the line whose equation is 2x-5y-10=0 and has the same y-intercept as this line.
The equation of the function is?
5y = 2x - 10 ... y = 2/5 x - 2
negative-reciprocal slope, same y-intercept
y = -5/2 x - 2
Well, if the graph of function f is perpendicular to the line 2x-5y-10=0, then we know that the slopes of the two lines are negative reciprocals. The slope of the given line is 2/5, so the slope of the graph of function f is -5/2.
Now, since the graph of f has the same y-intercept as the given line, we can determine the y-intercept of the given line. By rearranging the equation 2x - 5y - 10 = 0, we find that -5y = -2x + 10, which simplifies to y = (2/5)x - 2. So, the y-intercept of the given line is -2.
Plugging the slope (-5/2) and the y-intercept (-2) into the slope-intercept form y = mx + b, we have:
f(x) = (-5/2)x - 2
So, the equation of the function f is y = (-5/2)x - 2. Keep in mind that I'm just a humor bot, but I hope I still managed to help!
To find the slope-intercept equation of the function f, we first need to determine the slope of the given line. The given line has the equation 2x - 5y - 10 = 0.
To find the slope of this line, we rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept.
Starting with 2x - 5y - 10 = 0, we isolate the y-term:
-5y = -2x + 10
Dividing both sides by -5, we get:
y = (2/5)x - 2
The slope of the given line is therefore 2/5.
Since the graph of f is perpendicular to this line, the slope of f will be the negative reciprocal of the slope of the given line. The negative reciprocal of 2/5 is -5/2.
Now, we also know that f has the same y-intercept as the given line. Therefore, the y-intercept of f is -2.
Putting this information together, the slope-intercept equation of the function f is:
y = (-5/2)x - 2.
To find the slope-intercept equation of the function f, we first need to determine the slope of the given line. The equation of the given line is 2x - 5y - 10 = 0.
To put the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to solve the equation for y:
2x - 5y - 10 = 0
-5y = -2x + 10
y = (2/5)x - 2
The slope of the given line is (2/5). Since we want the graph of f to be perpendicular to this line, we can determine the perpendicular slope by taking the negative reciprocal of the given slope.
The negative reciprocal of (2/5) is -5/2.
Now we have the perpendicular slope, and we know that f has the same y-intercept as the given line. The y-intercept of the given line is -2.
Therefore, the slope-intercept equation of the function f is:
y = (-5/2)x - 2