Slope and y-intercept

The line x = 5 is vertical and parallel to the y-axis. To check a y-intercept, put x = 0; this is impossible in x = 5, so it never meets the y-axis. Exam tip: a vertical line has no y-intercept.

A line in the form y = mx + c has y-intercept c. Here, 4n - 5 = 23, so 4n = 28 and n = 7. Therefore, the slope is n - 7 = 7 - 7 = 0. Option 1 is not correct because substituting n = 7 makes the coefficient of x equal to zero. Exam tip: In y = mx + c, the coefficient of x is always the slope.

A line in the form y = mx + c has slope m, the coefficient of x. Here, the slope is t - 10. So, t - 10 = 5, giving t = 15. Therefore, the y-intercept is 3t - 1 = 3(15) - 1 = 44. Getting 43 would result from an arithmetic error in the final subtraction. Exam tip: first find the parameter using the slope, then substitute it into the constant term.

The slope is \(m=\frac{\Delta y}{\Delta x}=\frac{54}{6}=9\). The y-intercept is \(-14\), so substituting \(m=9\) and \(c=-14\) in \(y=mx+c\) gives \(y=9x-14\). Although \(y=54x-14\) has the correct intercept, its slope is 54, not 9. Exam tip: find the rate of change using \(\Delta y/\Delta x\).

When \(x\) increases by \(7\), \(y\) decreases by \(49\), so the slope is \(m=\frac{-49}{7}=-7\). The given \(y\)-intercept is \(18\). Substituting these in \(y=mx+c\) gives \(y=-7x+18\). Option C has slope \(-49\), which would mean that \(y\) decreases by 49 for every increase of 1 in \(x\). Exam tip: find slope using \(\Delta y/\Delta x\).

A line parallel to the \(y\)-axis is vertical, so its equation has the form \(x=\text{constant}\). Since the point has \(x\)-coordinate 3, the line is \(x=3\). \(y=-2\) is horizontal. Exam tip: a vertical line has undefined slope.

A line in the form y = mx + c has y-intercept c. Here, the y-intercept is u + 6. So, u + 6 = 16, giving u = 10. Therefore, the slope is 3u - 2 = 3(10) - 2 = 28. Option 26 can result from an incorrect subtraction. Exam tip: to find the y-intercept, put x = 0.

From (4y=-10x+44), (y=-\frac{5}{2}x+11). So the (y)-intercept is (11) and slope is (-\frac{5}{2}).

In the form y=mx+c, the y-intercept is c because substituting x=0 gives y=c. The first line has y-intercept b, while the second has y-intercept 13. Since they meet the y-axis at the same point, b=13. The values 8 and −6 are slopes, not y-intercepts. Exam tip: put x=0 to find a y-intercept.

In the form y = mx + c, the coefficient of x, m, is the slope. Since the two lines have equal slopes, a = 10. Substituting x = 3 in the first line gives y = 10(3) - 12 = 18. The value 20 would not account correctly for the constant term -12. Exam tip: for lines with equal slopes, compare the coefficients of x.

The y-intercept is the value of y when x=0, so c=7. Substituting x=-3 gives y=-11(-3)+7=33+7=40. The value 44 can result from incorrectly adding 11 to 33. Exam tip: identify the constant term from the y-intercept and carefully handle signs when multiplying negative numbers.

In \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept. For \(y=2x-5\), \(m=2>0\) and \(c=-5<0\). Although \(y=-2x-5\) has a negative intercept, its slope is negative too. Exam tip: check the coefficient of x first.

In \(y=mx+c\), \(m=-3\) is negative, so the line falls from left to right. Also, \(c=5\) is the y-intercept. Exam tip: identify the sign of slope and the constant term separately.

In slope-intercept form \(y=mx+c\), \(m\) is the slope and \(c\) is the y-intercept. For \(y=2x-3\), \(m=2\) and \(c=-3\). Option B has a negative slope. Exam tip: identify the coefficient of \(x\) and the constant term first.

In the equation of a line, the slope is represented by \(m\). Given \(m+c=21\) and \(c=8\), we get \(m+8=21\). Hence, \(m=21-8=13\). Therefore, the correct answer is 13. Note that 8 is \(c\), the y-intercept, not the slope. Exam tip: in \(y=mx+c\), the coefficient \(m\) is always the slope.

In the form \(y=mx+c\), \(m\) is the slope and \(c\) is the \(y\)-intercept. Given slope \(m=-7\), substitute it into \(m+c=5\): \(-7+c=5\). Hence, \(c=12\). Choosing \(-12\) would result from a sign error. Exam tip: add \(7\) to both sides to isolate \(c\).

For the given point, substitute \(x=12\) and \(y=19\): \(19=\frac{5}{6}\times 12+c\). Since \(\frac{5}{6}\times 12=10\), we get \(19=10+c\), so \(c=9\). Option 10 is the value of the slope term, not the y-intercept. Exam tip: in \(y=mx+c\), substitute both coordinates of the given point to find \(c\).

The given line \(y=-3x+5\) has slope \(-3\). Parallel lines must have the same slope. Also, in \(y=mx+c\), \(c\) is the y-intercept, which must be \(-2\) here. Therefore, the required equation is \(y=-3x-2\). Option C has the correct slope but its y-intercept is \(+2\). Exam tip: verify the slope first and then check the constant term for the y-intercept.

In the form \(y=mx+c\), the y-intercept is the constant term \(c\). Here, \(a+4=13\), so \(a=9\). Therefore, the slope is \(m=6a-5=6(9)-5=49\). Choosing 50 would result from incorrectly handling the subtraction of 5. Exam tip: first find the parameter using the y-intercept, then substitute it into the coefficient of \(x\).

In the form \(y=mx+c\), the coefficient of \(x\) is the slope. Thus, \(b-13=4\), giving \(b=17\). The \(y\)-intercept is the constant term \(3b+1\): \(3(17)+1=52\). Therefore, 52 is correct. The value 51 would result from using only \(3b\) and missing the \(+1\). Exam tip: first find the parameter from the slope, then substitute it into the constant term.