graph the line passing through the given point and having the given slope (2,-1) m=-6/5
To graph the line passing through the point (2, -1) and having a slope of -6/5, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope.
Plugging in the values, we have:
y - (-1) = (-6/5)(x - 2)
Simplifying:
y + 1 = (-6/5)x + 12/5
To put this equation in slope-intercept form (y = mx + b), subtract 1 from both sides:
y = (-6/5)x + 12/5 - 1
y = (-6/5)x + 12/5 - 5/5
y = (-6/5)x + 7/5
Now we have the equation in slope-intercept form, where the slope is -6/5 and the y-intercept is 7/5.
To graph this line, we can plot the given point (2, -1) and then use the slope to find additional points.
Starting with the point (2, -1), we can go down 6 units (since the slope is -6/5) and right 5 units to find another point. This gives us the point (7, -7).
Plotting these points and connecting them with a straight line, we get:
{{{graph(400,400,-10,10,-10,10,(-6/5)x + 7/5)}}}